A basketball player shoots toward a basket 5.6 m away and 3.0 m above the floor. If the ball is released 1.8 m above the floor at an angle of 60 o above the horizontal, what must the initial speed be if it were to go through the basket?

Answer:

[tex]T = 175.6 N[/tex]

Explanation:

As we know that string is vibrating in third harmonic

So we will have

[tex]L = 3\frac{\lambda}{2}[/tex]

so we have

[tex]0.79 = \frac{3}{2}\lambda[/tex]

so we have

[tex]\lambda = \frac{2}{3}(0.79)[/tex]

[tex]\lambda = 0.527[/tex]

we know that frequency of the wave is given as

f = 500 Hz

now we know that

speed of the wave is

[tex]v = frequency \times wavelength[/tex]

[tex]v = (500)(0.527)[/tex]

[tex]v = 263.3 m/s[/tex]

now we have

[tex]v = \sqrt{\frac{T}{m/L}}[/tex]

so we have

[tex]263.3 \sqrt{\frac{T}{(0.002/0.79)}}[/tex]

[tex]T = 175.6 N[/tex]

Answer:

Explanation: Ok, first caracterize the two vectors that we know.

A = ax + ay = (12*cos(40°)*i + 12*sin(40°)*j) m

now, see that C is angled 20° from -x, -x is angled 180° counterclockwise from +x, so C is angled 200° counterclockwise from +x

C = cx + cy = (15*cos(200°)*i + 15*sin(200°)*j) m

where i and j refers to the versors associated to te x axis and the y axis respectively.

in a sum of vectors, we must decompose in components, so: ax + bx  = cx and ay + by = cy. From this two equations we can obtain B.

bx= (15*cos(200°) - 12*cos(40°)) m = -23.288 m

by = (15*sin(200°) - 12*sin(40°)) m = -12.843 m

Now with te value of both components of B, we proceed to see his magnitude an angle relative to +x.

Lets call a to the angle between -x and B, from trigonometry we know that tg(a) = by/bx, that means a = arctg(12.843/23.288) = 28.8°

So the total angle will be 180° + 28.8° = 208.8°.

For the magnitude of B, lets call it B', we can use the angle that we just obtained.

bx = B'*cos(208.8°) so B' = (-23.288 m)/cos(208.8°) =  26.58 m.

So the magnitude of B is 26.58 m.

Final answer:

The magnitude of vector B is 3.0 m and its angle relative to +x direction is 60.0°.

Explanation:

To find the magnitude and angle of vector →B, we can use vector addition. The magnitude of →B can be found using the equation:

|→B| = |→C| - |→A|

Substituting the given magnitudes, we have:

|→B| = 15.0 m - 12.0 m = 3.0 m

Next, we can find the angle of →B using trigonometry. Since →A is angled 40.0° counterclockwise from the +x direction, and →C is angled 20.0° counterclockwise from the −x direction, the angle of →B can be found by subtracting these angles:

θ = (20.0° - (-40.0°)) = 60.0°

Therefore, the magnitude of →B is 3.0 m and its angle relative to the +x direction is 60.0°.

Answer:

Correct option is (C)

Explanation:

u = 0 m/s

a = 5 m/s^2

(a) Distance traveled by the particle in first second

s = ut + 1/2 at^2

s = 0 + 0.5 x 5 x 1 x 1 = 2.5 m

So, this option is wrong.

(b) As we observe by the part (a) that the particle travels a distance of 2.5 m in first second so, this option is wrong.

(c) The acceleration of the particle is 5m/s^2, it means the speed of teh particle increases by 5 m/s every second. So, this is true.

(d) As we observe by part (c), the speed of the particle increases by 5 m/s every second so this option is wrong.  

The correct statement that describes the motion of a particle accelerating at a rate of 5.0 m/s^2 from rest is that the speed of the particle increases by 5.0 m/s during each second, based on the basic kinematics equation.

The subject of this question falls under Physics, specifically kinematics. The statement that accurately describes the motion of the particle is option c. "The speed of the particle increases by 5.0 m/s during each second." This is because acceleration is defined as the change in velocity or speed per unit time. So if the particle is accelerating at a rate of 5.0 m/s2, this means its speed increases by 5.0 m/s for every second that passes.

This can be understood by the basic kinematic equation: v = u + at, where v is the final velocity, u is the initial velocity (which is zero in this case, as the particle is starting from rest), a is the acceleration and t is the time. So, each second, the speed increases by the acceleration, which in this case is 5 m/s.

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Answer:

Bow Line

Explanation:

If the wind or current is pushing your boat away from the dock, bow line should be secured first.

1- We should cast off the bow and stern lines.

2-With the help of an oar or boat hook, keep the boat clear of the dock.

3-Leave the boat on its own for sometime and let the wind or current carry the boat away from the dock.

4 - As you see there is sufficient clearance, shift into forward gear and slowly leave the area.

Answer:

a. 8.3 minutes average distance from earth to the sun

d. 93 miles or 150 million km

Explanation:

The distance between the earth and the sun is defined as an astronomical unit (AU). It takes 8.3 minutes to go from earth to the sun at the speed of light. That distance has a length of 150 million Kilometers or 93 miles.  

It is common to see in planet charts that distance to the sun are compared in astronomical units. In the case of Mars is 1.524 AU away from the sun.

Answer:

(a) 52.724 m/s

(b) Total displacement, d = 551.25 m

Solution:

As per the question:

Initial acceleration of the speed boat, a = - 2.01 [tex]m/s^{2}[/tex]

Time duration, t = 7.00 s

Additional time, t' =6.00 s

Acceleration for additional time, a' = 0.518 [tex]m/s^{2}[/tex]

The followed up acceleration, a'' = 1.49 [tex]m/s^{2}[/tex]

Time duration, t'' = 8.00 s

(a) Now, to calculate the velocity of the boat at timer, t = 21.0 s, we have:

After the initial 7.00 s, the velocity of the boat, from eqn-1 of motion:

v = u + at

v = 0 - 2.1(7.00) = - 14.7 m/s

After t + t' = 13 s:

v' = v + at

v' =  14.7 + 0.518(13) =  21.434 m/s

Now, velocity of the boat after t = 21 s:

v'' = v' + a''t

v'' = 21.434 + 1.49(21) = 52.724 m/s

(b) Now, the total displacement, d:

For the first case:

d = ut + [tex]\frac{1}{2}at^{2} = 0 - 0.5\times 2.1\times 7^{2} = - 51.45 m[/tex]

For the second case:

d = v't' = 21.434(6) = 128.6 m

For the third case:

d = ut + [tex]\frac{1}{2}a't'^{2} = 0 + 0.5\times 0.518\times 6^{2} = 4.65 m[/tex]

For the fourth case:

d = v''t'' = 52.724(8) = 421.79 m

For the last case:

d = ut + [tex]\frac{1}{2}a't'^{2} = 0 + 0.5\times 1.49\times 8^{2} = 47.68 m[/tex]

Total displacement, d = -51.45 + 128.6 + 4.65 + 421.79 + 47.68 = 551.25 m

Answer:

speed of current is 5 mile/hr

Explanation:

GIVEN DATA:

speed of motorboat = 15 miles/hr relative with water

let c is speed of current

15-c is speed of boat at  upstream

15+c is speed of boat at downstream

we know that

travel time=distance/speed

[tex]\frac{10}{15-c} +\frac{10}{15+c} = 1.5[/tex]

150+10c+150-10c=1.5(15-c)(15+c)

300=1.5(225-c^2)

300=337.5-1.5c^2

200=225-c^2

c^2=25

c = 5

so speed of current is 5 mile/hr

Final answer:

To find the speed of the current for a boat trip upstream and downstream taking a total of 1.5 hours at a constant speed of 15 mph relative to the water, we derive and solve an equation based on time taken for each part of the journey. The solution reveals that the current's speed is 3 mph.

Explanation:

The student asked how to find the speed of the current when a motorboat, traveling at a constant speed of 15 miles per hour relative to the water, went 10 miles upstream and then returned downstream, with the total trip taking 1.5 hours.

Step-by-Step Solution

By solving the equation, we find that the speed of the current is 3 miles per hour.

The magnitude of the magnetic field at the center of the solenoid is 2π x 10^-5 Tesla, found using the formula B = μ₀nI and assuming the length of the solenoid can be estimated from the diameter of the wire and the number of turns.

To calculate the magnetic field inside a solenoid, we use Ampere's law, which is in the form B =
μ₀nI when the core is air. The term μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current. Just by looking at the problem, we don't need to use the diameter of the wire, as the number of turns per unit length (n) is the critical value needed in the formula and they are given directly.

The number of turns per unit length can be found by dividing the number of turns by the length of the solenoid. However, the length of the solenoid is not provided, so we would typically divide the number of turns (200) by the solenoid's length. Assuming that the coils are tightly wound with adjacent coils touching and the diameter of the wire is 2.0 mm, the length can be estimated as the diameter times the number of turns (0.002 m * 200 = 0.4 m).

So, substituting the values into the equation B = μ₀nI, where μ₀ = 4π x 10^-7 T·m/A, n = 200 turns / 0.4 m = 500 turns/m, and I = 0.10 A, we get:

B = (4π x 10^-7 T·m/A) * (500 turns/m) * (0.10 A) = 2π x 10^-5 (T)

Thus, the magnitude of the magnetic field at the center of the solenoid is 2π x 10^-5 Tesla.

Answer:

Explanation:

mass, m = 43 g = 0.043 kg

L = 81 cm = 0.81 m

frequency, f = 59 Hz

Amplitude, A = 0.35 cm

(a)

Frequency

[tex]f=\frac{v}{2L}[/tex]

v = 59 x 2 x 0.81 = 95.58 m/s

(b)

Let F be the tension in the string

[tex]v=\sqrt{\frac{F}{\mu }}[/tex]

where, μ is mass per unit length

[tex]\mu =\frac{0.043}{0.81}=0.053 kg/m[/tex]

[tex]95.58=\sqrt{\frac{F}{0.053 }}[/tex]

[tex]F = 95.58\times 95.58 \times 0.053[/tex]

F = 484.18 N

(c)

Maximum velocity

v = ω A = 2 π f A

v = 2 x 3.14 x 59 x 0.0035 = 1.3 m/s

(d)

Maximum acceleration

a = ω² A

a = (2 π f )² x 0.0035

a = ( 2 x 3.14 x 59)² x 0.0035

a = 480.5 m/s^2

Answer:

The answer to your question is:  magnitude:  1534.9 units

direction: 326.5°

Explanation:

Data

x = 1280 u

y = -847 y

Then as x is positive and y is negative this vector is quadrangle

To find the magnitude, we use the pythagorean theorem

c2 = a2 + b2

c2 = 1280² + (-847)² = 1638400 + 717409 = 2355809

c = 1534.9 units

to find the direction we use the tangent function

tanФ = os/as = -847/1280 = -0.661

Ф = 33.49

But it is in the 4th quadrangle, then

Ф = 360 - 33-49 = 326.5°

Answer:

1530 units, -33.5°

Explanation:

Given the x-component and the y-component, the magnitude can be found with Pythagorean theorem:

v² = vx² + vy²

And the direction can be found with trigonometry:

θ = atan(vy / vx)

Given that vx = 1280 and vy = -847:

v² = (1280)² + (-847)²

v ≈ 1530

θ = atan(-847 / 1280)

θ ≈ -33.5° or 146.5°

θ is in the fourth quadrant, so θ = -33.5°.

Answer:

13.7 s

Explanation:

The position at time t of car A can be written as follows:

[tex]x_A (t) = \frac{1}{2}a_At^2[/tex]

where

[tex]a_A = 11 m/s^2[/tex] is the acceleration of car A

The position of car B instead can be written as

[tex]x_B(t) = d+\frac{1}{2}a_B t^2[/tex]

where

[tex]a_B = -4 m/s^2[/tex] is the acceleration of car B

d = 1400 m is the initial separation between the cars

The two cars meet when

[tex]x_A = x_B[/tex]

Using the two equations above,

[tex]\frac{1}{2}a_A t^2 = d + \frac{1}{2}a_B t^2\\\frac{1}{2}t^2 (a_A - a_B) = d\\t=\sqrt{\frac{2d}{a_A-a_B}}=\sqrt{\frac{2(1400)}{11-(-4)}}=13.7 s[/tex]

Final answer:

The two cars with given accelerations and an initial distance of 1400 meters between them when starting from rest will meet after 20 seconds.

Explanation:

To solve for the time at which the two cars meet, we must consider the accelerations of both cars and the initial distance between them. Assuming car A is moving with a positive acceleration of 11 m/s2 and car B is moving with a negative acceleration of -4 m/s², we need to find a common point in time where they both cover the total distance of 1400 m when starting from rest.

Let the time taken for the cars to meet be denoted by 't'. For car A, the displacement (sA) is given by the formula sA = 0.5 * aA * t², and for car B, the displacement (sB) is given by sB = 0.5 * aB * t². As they are moving towards each other, the sum of their displacements sA+sB should equal the initial separation distance which is 1400m.

This gives us the equation 0.5 * 11 * t2 + 0.5 * (-4) * t² = 1400. Simplifying, we get 3.5 * t² = 1400, and solving for 't' gives us t2 = 400, so t = 20 seconds. Hence, both cars will meet after 20 seconds.

Answer:

Restoring force of the spring is 50 N.

Explanation:

Given that,

Spring constant of the spring, k = 100 N/m

Stretching in the spring, x = 0.5 m

We need to find the restoring force of the spring. It can be calculated using Hooke's law as "the force on a spring varies directly with the distance that it is stretched".

[tex]F=kx[/tex]

[tex]F=100\ N/m\times 0.5\ m[/tex]

F = 50 N

So, the restoring force of the spring is 50 N. Hence, this is the required solution.

Answer:angle of ramp

Explanation:

The acceleration of a cart rolling down a ramp depends on the angle of the ramp and not on the length of the ramp.

Let the car have wheel in form of thin cylinder, therefore its acceleration is given by

[tex]a=\frac{gsin\theta }{1+\frac{I}{mr^2}}[/tex]

where

a=acceleration

g=acceleration due to gravity

I=moment of inertia of the wheel

m=mass of wheel

r=radius of wheel

[tex]\theta [/tex]=angle made by ramp with the horizontal

In above term there is no sign of length of ramp thus it is independent of it.

The acceleration of a cart rolling down a ramp is primarily influenced by the angle of the incline and gravitational acceleration, but in practical scenarios, friction and other factors also play a role. The final velocity as the cart leaves the ramp is a function of the acceleration and the distance over which it acts.

The acceleration of a cart rolling down a ramp depends on several factors, including the angle of the incline and the presence of friction. When considering a cart on a frictionless inclined plane, the acceleration only depends on the angle of the ramp and gravitational acceleration. However, in real-world scenarios, factors such as friction, the mass of the cart, and the initial velocity may also play a role. Acceleration is directly related to the sine of the angle of the incline. Furthermore, the final velocity of the cart as it leaves the ramp would depend on both the acceleration of the cart down the ramp and the distance over which the acceleration acts. In the absence of air resistance, all objects slide down a frictionless incline with the same acceleration if the angle is the same. Also, linear and angular accelerations are directly proportional, with the radius of wheels also affecting the acceleration.

Answer:

Option D.

Explanation:

The first law of thermodynamics is a law of conservation of energy. This automatically tells us that energy lost by a system won't dissapear, but it will be gained by the surroundings.

Mathematically is stated this way:

ΔU=Q-W

Where ΔU is the change in the internal energy of a closed system, Q is the amount of heat supplied and W the amount of work done by the system on its surroundings. It means that if the internal energy U decreases, then that energy lost must have been converted to work W in the surroundings.

The first law of thermodynamics is best represented by the statement: Energy lost by the system must be gained by the surroundings.

The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed but it can be transformed from one form to another. The most accurate representation of the first law of thermodynamics from the provided options is [D] Energy lost by the system must be gained by the surroundings. This statement effectively communicates the balance of energy transfer which is fundamental to understanding the concept of first law of thermodynamics.

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To find the time it takes for the baseball to reach the ground, we can use the equations of motion for an object in free fall. We can solve a quadratic equation to find the time and then use it to find the final velocity of the baseball when it strikes the ground.

To solve this problem, we can use the equations of motion for an object in free fall. The object is thrown downward, so the initial velocity is negative. We can use the equation: h = ut + (1/2)gt² to find the time taken to reach the ground. In this equation, h is the height, u is the initial velocity, t is the time, and g is the acceleration due to gravity. Since the initial height is 555 ft and the initial velocity is 40 ft/s, the equation becomes 555 = -40t + (1/2)(32)(t²). We can solve this quadratic equation to find the time it takes for the baseball to reach the ground. Once we have the time, we can use the equation: v = u + gt to find the final velocity. Plugging in the values, we get v = 40 + (32)t. Substitute the value of t from the first equation to find the final velocity when the baseball strikes the ground.

Answer:

It will take 15.55s for the police car to pass the SUV

Explanation:

We first have to establish that both the police car and the SUV will travel the same distance in the same amount of time. The police car is moving at constant velocity and the SUV is experiencing a deceleration. Thus we will use two distance fromulas (for constant and accelerated motions) with the same variable for t and x:

1. [tex]x=x_{0}+vt[/tex]

2. [tex]x=x_{0}+v_{0}t+\frac{at^{2}}{2}[/tex]

Since both cars will travel the same distance x, we can equal both formulas and solve for t:

[tex]vt = v_{0}t+\frac{at^2}{2}\\\\   16\frac{m}{s}t =30\frac{m}{s}t-\frac{1.8\frac{m}{s^{2}} t^{2}}{2}[/tex]

We simplify the fraction present and rearrange for our formula so that it equals 0:

[tex]0.9\frac{m}{s^{2}} t^{2}-14\frac{m}{s}t=0 \\\\ t(0.9\frac{m}{s^{2}}t-14\frac{m}{s})=0[/tex]

In the very last step we factored a common factor t. There is two possible solutions to the equation at [tex]t=0[/tex] and:

[tex]0.9\frac{m}{s^{2}}t-14\frac{m}{s}=0 \\\\  0.9\frac{m}{s^{2}}t =14\frac{m}{s} \\\\ t =\frac{14\frac{m}{s}}{0.9\frac{m}{s^{2}}}=15.56s[/tex]

What this means is that during the displacement of the police car and SUV, there will be two moments in time where they will be next to each other; at [tex]t=0 s[/tex] (when the SUV passed the police car) and [tex]t=15.56s[/tex](when the police car catches up to the SUV)

-- Gravity slows the ball by 9.8 m/s every second. So it slows to zero and reached its highest point in

(58.8 / 9.8) = 6 seconds .

-- Its average speed all the way up is

(1/2) (58.8 + 0) = 29.4 m/s

-- Traveling for 6 seconds at an average speed of 29.4 m/s, the ball covers

(6) (29.4) = 176.4 meters .

Answer:

Matter have two essential types of properties, those are physical properties and chemical properties.

Explanation:

Answer:

Explanation:

Gotta work on writing the problem, kida hard to read with the coding text.  Anyway, a rectangle with one side  of 6 cm and another  at 3.5 cm, then rectangle B is proportional to that.  Which basically means rectangle B will be multiplied or divided by some number.

To make the concept a little simpler imagine it was a square with sides of length 2.  a proportional square twice as big would have lengths of 4 and half as big would have lengths of 1.

In this case we need measurements where one is 6 multiplied or divided by a number x, and then 3.5 has the same action done on it with the same number.  so again, twice as big would be 12 and 7 while half as big would be 3 and 1.75  anyway, let's look at the options.

A) 3 and 1.75

B) 5 and 2.5

C) 7 and 7

D) 12 and 5

E) 5.25 and 9

Just to have ti written, the original rectangle is 6 by 3.5

So A is obvious since I used it as an example, this is a proportional rectangle half the size of A.

The rest are harder to check except C.  7 and 7 make a square, but we know the side lengths have to be different, so C is easy to tell it's not right.

B we have to check.  Since it's not as obvious as A, we have to check with math more carefully.  What do we have to multiply 6 by to get 5?  Also, you always want to make the largest side of each rectangle proportional to each other.  Anyway, 6 times 5/6 is 5, so for B to be right, 3.5 times 5/6 needs to be equal to 2.5.  Does it?  Nope, its 2.9166 repeating.  So B is not right.

I'm not going to go through so much explanation for the others, if you don't get something let me know.  

D we could also know quickly isn't right since I told you the measurements if the rectangle is changed to one with a side length of 12.  We would need the other to be 7, so 12 and 5 isn't right.

E is our last possibility, since we need to pick two, but let's check anyway.  we need to multiply 6 by 7/8 to get 5.25.  3.5 times 7/8 is 3.0625, so not 9.  Good thing we checked here, because only one answer looks to be right.  Are you sure you put the right numbers?  Or did I misinterpret some?  

Answer:

A and E

Explanation:

Answer:

721.8 Joule per second

Explanation:

L = 33 cm = 0.33 m

A = 55 cm^2 = 0.0055 m^2

Th = 129°C

Tc = 21°C

k = 401 W/mK

The rate of flow of heat is given by the formula

[tex]H =\frac{K A \left ( T_{h}-T_{c} \right )}{L}[/tex]

[tex]H =\frac {401  \times 0.0055 \times \left (129-21\right )}{0.33}[/tex]

H = 721.8 Joule per second

Thus, the rate of flow of heat is given by 721.8 Joule per second.

Final answer:

To find the conduction rate through the slab, use the formula Q/t = kA(TH - TC)/L. With the given values for copper's thermal conductivity, area, thickness, and temperature difference, the conduction rate is calculated to be 74,454 Watts or 74.454 kW.

Explanation:

To find the conduction rate through a copper slab, we can use the formula for heat transfer through conduction: Q/t = kA(TH - TC)/L. In this formula, Q/t is the rate of heat transfer (conduction rate), k represents the thermal conductivity of copper, A is the surface area of the slab, TH and TC are the temperatures of the hot and cold faces respectively, and L is the thickness of the slab.

Using the given values, L = 0.33 m (converted from 33 cm), A = 0.0055 m2 (converted from 55 cm2), k = 401 W/m·K, TH = 129°C, and TC = 21°C, the conduction rate can be calculated as follows:

Q/t = 401 W/m·K × 0.0055 m2 × (129°C - 21°C) / 0.33 m

Q/t = 401 W/m·K × 0.0055 m2 × 108 K / 0.33 m

Q/t = 74,454 W/m·K × m2 / m

Q/t = 74,454 W

Therefore, the conduction rate through the copper slab is 74,454 Watts or 74.454 kW.

Answer:

723.54 N

Explanation:

Weight of anchor = 833 N

density of iron = 7800 mg/m^3

density of sea water = 1025 kg/m^3

According to the Archimedes principle, if a body is immersed wholly or partly in a liquid it experiences a loss in weight of the body which is equal to the weight of liquid displaced by the body.

The loss in the weight of body is equal to the buoyant force acting on the body.

The formula for the buoyant force acting on the body

= volume of body x density of liquid x acceleration due to gravity

Weight of anchor = mass x acceleration due to gravity

833 = m x 9.8

m = 85 kg

mass of anchor = Volume of anchor x density of iron

85 = V x 7800

V = 0.01089 m^3

Buoyant force on the anchor = Volume of anchor x density of sea water x g

                                               = 0.01089 x 1025 x 9.8 = 109.46 N

So, the tension in the chain = Apparent weight of the anchor

                                              = Weight - Buoyant force

                                              = 833 - 109.46 = 723.54 N

Thus, the tension in the chain is 723.54 N.

Final answer:

Around 13.14% of an iron anchor's weight will be supported by buoyant force when it is submerged in saltwater, calculated based on the densities of iron and seawater.

Explanation:

The question revolves around determining what fraction of an iron anchor's weight will be supported by buoyant force when it is submerged in saltwater. The buoyant force acting on any object submerged in a fluid is equal to the weight of the fluid displaced by the object. This principle is articulated by Archimedes' principle. For the iron anchor, the fraction supported by the buoyant force is directly linked to the densities of iron (7800 kg/m3) and the seawater (1025 kg/m3) in which it is submerged.

To find this fraction, we use the formula: Fraction Supported = Density of Seawater / Density of Iron.

Therefore, Fraction Supported = 1025 / 7800 ≈ 0.1314.

So, when an iron anchor is submerged in seawater, approximately 13.14% of its weight is supported by the buoyant force.

Answer:

[tex]3,666,500\ m^3 = 3.666\times 10^9\ Liters[/tex]

Explanation:

Given that

Volume

[tex]V=3,666,500\ m^3[/tex]

As we know that

[tex]1\ m^3 = 1000\ Liters[/tex]

[tex]1\ m^3 = 10^3\ Liters[/tex]

So

[tex]3,666,500\ m^3 = 3,666,500\times 10^3\ Liters[/tex]

[tex]3,666,500\ m^3 = 3,666,5\times 10^5\ Liters[/tex]

[tex]3,666,500\ m^3 = 3.666\times 10^9\ Liters[/tex]

So we cab say that [tex]3,666,500\ m^3[/tex] is equal to [tex]3.666\times 10^9\ Liters[/tex].

Answer:

The answer to your question is below

Explanation:

Data

light speed = 300 000 km/s

a) Express it in scientific notation

to do it, we just move the decimal point 5 places to the left

         300 000 = 3.0 x 10 ⁵ km/s

b) Convert this value to meters per hour

  (300 000 km/s)(1000 m/1 km)(3600 s/1 h) = 300000x1000x3600 / 1x1x1

                                                                        = 1.08 x 10¹² m/h

c) What distance in centimeters does light travel in 1 s?

data

v = 300 000 km/s

d = ?

t = 1 s

 formula   v = d/t      we clear distance     d = vxt

                                  d = 300000 x 1 = 300000 km

                                   d = 300000000 m = 30000000000 cm

A. Expression of 300000 km/s in scientific notation.

Scientific notation is a most reliable way of writing a very large or very small number in a convenient way.

To express 300000 km/s in scientific notation, move the decimal point from the last zero number to the non zero number. Include a multiple of 10 raised to power of the number of move as shown below:

Number to express = 300000 Km/s

The Non zero number is => 3

Number of moves = 5

Therefore, the scientific notation of 300000 Km/s is 3.0 × 10⁵ Km/s

B. Converting 300000 Km/s to m/h

We'll begin by converting 300000 Km/s to m/s. This can be obtained as follow :

1 Km/s = 1000 m/s

Therefore,

[tex]300000 Km/s =\frac{300000 Km/s * 1000 m/s}{1 Km/s } \\[/tex]

Finally, we shall convert 300000000 m/s to m/h

1 m/s = 3600 m/h

Thus,

[tex]300000000 m/s = \frac{300000000 m/s * 3600 m/h}{1 m/s}[/tex]

Therefore,

C. Determination of the distance (in cm)  travelled in 1 second.

We'll begin by converting 300000 km/s to cm/s.

This can be obtained as follow:

1 km/s = 100000 cm/s

Therefore,

[tex]300000 km/s = \frac{300000 km/s * 100000 cm/s }{1 km/s} \\[/tex]

Finally, we shall determine the distance (in cm). This can be obtained as follow:

Speed = 3×10¹⁰ cm/s

Time = 1 s

[tex]Speed = \frac{Distance}{Time}\\\\3*10^{10} = \frac{Distance}{1}[/tex]

Cross multiply

Distance = 3×10¹⁰ × 1

Therefore, light travels a distance of 3×10¹⁰ cm in 1 second.

Learn more: https://brainly.com/question/13585060

Answer:

127.36 m/s

Explanation:

velocity of plane with respect to air = 140 m/s due east

velocity of air with respect to ground = 31 m/s 30° west of north

Write the velocities in the vector forms

[tex]\overrightarrow{V_{p/a}}=140\widehat{i}[/tex]

[tex]\overrightarrow{V_{a/g}}=31  \left ( -Sin30 \widehat{i}+Cos30\widehat{j} \right )[/tex]

[tex]\overrightarrow{V_{a/g}}= -15.5 \widehat{i}+26.85\widehat{j}[/tex]

Let velocity of plane with respect to ground is given by vp/g

According to the formula of relative velocities

[tex]\overrightarrow{V_{p/a}}=\overrightarrow{V_{p/g}}-\overrightarrow{V_{a/g}}[/tex]

[tex]\overrightarrow{V_{p/g}}=\overrightarrow{V_{p/a}}+\overrightarrow{V_{a/g}}[/tex]

[tex]\overrightarrow{V_{p/g}}= \left ( 140-15.5 \right )\widehat{i}+26.85\widehat{j}[/tex]

[tex]\overrightarrow{V_{p/g}}= \left ( 124.5 \right )\widehat{i}+26.85\widehat{j}[/tex]

The magnitude of the velocity of plane with respect to the ground is given by

[tex]V_{p/g} = \sqrt{124.5^{2}+26.85^{2}}=127.36 m/s[/tex]

Thus, the velocity of plane with respect to the ground is given by 127.36 m/s.

Answer:

There is an attractive force between the rod and sphere.

Explanation:

When negatively charged rod is placed close to the metal sphere then due to the electric field of the rod the opposite free charge of metal sphere comes closer to the rod on one surface

While similar charge in the metal sphere move away from the rod due to repulsion of electric field of rod

This temporary charge distribution of the metal sphere is known as induction

And since opposite charge on the metal surface comes closer to the metal sphere so here we can say that the rod will attract the metal sphere

so here correct answer will be

There is an attractive force between the rod and sphere.

Answer:

There is an attractive force between the rod and sphere.

Explanation:

Answer:

The net force acting on an object is the sum of all the force acting on it, and the net force of an object is zero. I f the forces acting on it tend to cancel each other. For example you are sit in a chair, the earth's gravity is pulling you down, but the chair is pushing you up with an equal amount of force.

Explanation:

Answer:

The net force acting on an object is the sum of all the force acting on it, and the net force of an object is zero. I f the forces acting on it tend to cancel each other. For example you are sit in a chair, the earth's gravity is pulling you down, but the chair is pushing you up with an equal amount of force.

Explanation:

science teacher helped me

Answer:

The distance moved is 9 meters

The magnitude of the displacement is 2.4 meters

The direction of the displacement is northward

Explanation:

- Distance is the length of the actual path between the initial and the

  final position. Distance is a scalar quantity

- Displacement is the change in position, measuring from its starting

  position to the final position. Displacement is a vector quantity

The quarterback pedals 3.3 meters southward

That means it moves down 3.3 meters

Then runs 5.7 meters northward

That means it runs up 5.7 meters

The distance = 3.3 + 5.7 = 9 meters

The distance moved is 9 meters

It moves southward (down) for 3.3 meters and then moves northward

(up) for 5.7

It moves from zero to 3.3 down and then moves up to 5.7

The displacement = 5.7 - 3.3 = 2.4 meters northward

The magnitude of the displacement is 2.4 meters

The direction of the displacement is northward

Final answer:

The quarterback moved a total distance of 9.0 meters. The displacement of the quarterback was 2.4 meters northward, as displacement takes into account the direction of motion.

Explanation:

When considering the movement of a quarterback who backpedals 3.3 meters southward and then runs 5.7 meters northward, we need to determine both the total distance moved and the magnitude and direction of the displacement.

The distance is a scalar quantity that represents the total path length traveled, regardless of direction. In this case, the quarterback moved a total distance of 3.3 meters + 5.7 meters = 9.0 meters.

On the other hand, displacement is a vector quantity, which means it has both magnitude and direction. To find the quarterback's displacement, we subtract the southward movement from the northward movement, because these movements are in opposite directions. The displacement is thus 5.7 meters - 3.3 meters = 2.4 meters northward.

Explanation:

When an object is moving in a circular path, the motion of the object is called uniform circular motion. The object moves under the action of centripetal acceleration. It is given by :

[tex]a=\dfrac{v^2}{r}[/tex]

r is the radius of circular path

v is the speed of the object

In uniform circular motion, the object moves with constant speed. Also, the velocity of the object keeps on changing because it changes direction at every instant of time. Also, the object is accelerating due to change in velocity.

So, the correct options are (b) and (c).

In uniform circular motion, an object travels in a circular path at a constant speed, but its velocity is not constant because the direction of motion changes. Thus, the object is accelerating due to the continuous change in direction, despite the speed being constant.

Understanding Uniform Circular Motion

Uniform circular motion refers to the motion of an object traveling in a circular path at a constant speed. This situation presents a peculiar form of acceleration. Even though the object maintains a constant speed, its velocity is not constant because its direction is continually changing.

The three statements provided, when evaluated, give us the following insights:

Therefore, the correct statements about an object in uniform circular motion are that it moves at a constant speed and it is indeed accelerating.

Answer:

25.2 s

Explanation:

In an uniformly accelerated motion starting from rest, the time taken for the motion is given by the equation

[tex]d=\frac{1}{2}at^2 \rightarrow t=\sqrt{\frac{2d}{a}}[/tex]

where t is the time, d is the distance covered, a is the acceleration.

We also know that the acceleration can be found by using Newton's second law:

[tex]\sum F = ma \rightarrow a=\frac{\sum F}{m}[/tex]

where [tex]\sum F[/tex] is the net force on the object and m its mass. Substituting into the previous equation,

[tex]t=\sqrt{\frac{2md}{\sum F}}[/tex] (1)

So we see that the time taken for the motion is inversely proportional to the square root of the net force.

Let's consider now the space probe in the problem. Let's call F the magnitude of the force generated by each engine.

When the two forces are applied in the same direction, the net force on the space probe is

[tex]\sum F = F+F = 2F[/tex]

But when the two forces are applied perpendicularly, the net force is

[tex]\sum F' = \sqrt{F^2+F^2}=\sqrt{2} F[/tex]

Using eq.(1) we can write:

[tex]\frac{t}{t'}=\sqrt{\frac{\sum F'}{\sum F}}[/tex]

where t' is the new duration of the motion. Solving for t',

[tex]t'=\sqrt{\frac{\sum F}{\sum F'}}t=\sqrt{\frac{2F}{\sqrt{2}F}}(21.2 s)=25.2 s[/tex]

Answer:3.67 m/s

Explanation:

mass of block(m)=2 kg

Velocity of block=6 m/s

spring constant(k)=2 KN/m

Spring compression x=15 cm

Conserving Energy

energy lost by block =Gain in potential energy in spring

[tex]\frac{m(v_1^2-v_2^2)}{2}=\frac{kx^2}{2}[/tex]

[tex]2\left [ 6^2-v_2^2\right ]=2\times 10^3\times \left [ 0.15\right ]^2[/tex]

[tex]v_2=3.67 m/s[/tex]