Julia can swim at 3.5 km/h in still water. She attempts to head straight north
across a river with a current flowing at 1.2 km/h West. What is her resultant
velocity? 

In this problem , at what angle should Julia aim in order to land directly across the
river from her start point?

The problem corresponds to the motion of a projectile (the salmon), with initial speed [tex]v_0[/tex], initial direction [tex]\theta=37.6^{\circ}[/tex] and vertical acceleration [tex]g=9.81 m/s^2[/tex] downward. The two equations which gives the horizontal and vertical position of the salmon at time t are

[tex]S_x (t) = v_0 cos \theta t[/tex] (1)

[tex]S_y (t) = v_0 sin \theta t - \frac{1}{2}gt^2[/tex] (2)

We can solve the problem by requiring Sx=3.16 m and Sy=0.379 m, the data of the problem.

Solving eq.(1) for t:

[tex]t=\frac{S_x}{v_0 cos \theta}[/tex]

And substituting this expression of t into eq.(2), we get the following expression for [tex]v_0[/tex]:

[tex]v_0 =\sqrt{\frac{g S_x^2}{2(tan \theta S_x -S_y)cos^2 \alpha}}[/tex]

And substituting the numbers into the equation, we find

[tex]v_0 = 6.16 m/s[/tex]

The minimum speed Salmon must jump is [tex]\boxed{6.16{\text{ }}{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}}[/tex].

Further explain:

Here, the given problem is on the basis of the projectile motion.

Given:

Initial direction [tex]\left( \theta\right)[/tex] with horizontal is [tex]37.6^\circ[/tex].  

The distance travel by Salmon in x-direction at time [tex]t[/tex] is [tex]3.16{\text{ m}}[/tex].

The distance travel by Salmon in y-direction at time [tex]t[/tex] is [tex]0.379{\text{ m}}[/tex].  

Acceleration due to gravity is [tex]9.8{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {{{\text{s}}^2}}}} \right. \kern-\nulldelimiterspace} {{{\text{s}}^2}}}[/tex].  

Formula and concept used:

The velocity component in x-direction [tex]\left( {{v_x}} \right)[/tex] is[tex]v\cos \theta[/tex].  

Distance travel by Salmon in x-direction at time [tex]t[/tex] is,

[tex]\begin{gathered}{s_x} = {v_x}t \hfill \\{s_x} = v\cos \theta\cdot t \hfill \\ \end{gathered}[/tex]

Simplify above equation,

[tex]\boxed{t=\dfrac{{{s_x}}}{{v\cos \theta }}}[/tex]                           …… (1)

The velocity component in y-direction[tex]\left( {{v_y}} \right)[/tex] is [tex]v\sin \theta[/tex].  

Distance travel by Salmon in y-direction at time [tex]t[/tex] is,

[tex]{s_y} = {v_y}t - \frac{1}{2}g{t^2}[/tex]

Substitute the value of [tex]{v_y}[/tex] in above equation,

[tex]\boxed{{s_y} = v\sin \theta\cdot t - \frac{1}{2}g{t^2}}[/tex]                       …… (2)

Substitute the value of [tex]t[/tex] from equation (1) in to the equation (2).

[tex]\begin{aligned}{s_y}&=v\sin \theta\cdot \left( {\frac{{{s_x}}}{{v\cos \theta }}} \right) - \frac{1}{2}g{\left( {\frac{{{s_x}}}{{v\cos \theta }}} \right)^2} \hfill \\&={s_x}\tan\theta- \frac{{g{{\left( {{s_x}} \right)}^2}}}{{2{v^2}{{\cos }^2}\theta}}\hfill\\\end{aligned}[/tex]

Simplify the above equation to obtain the value of [tex]v[/tex] ,

[tex]\dfrac{{g{{\left( {{s_x}} \right)}^2}}}{{2{v^2}{{\cos }^2}\theta }}={s_x}\tan \theta-{s_y}[/tex]

Rearrange the above expression.

[tex]\dfrac{1}{{{v^2}}}=\dfrac{{2{{\cos }^2}\theta\cdot \left( {{s_x}\tan\theta- {s_y}} \right)}}{{g{{\left( {{s_x}} \right)}^2}}}[/tex]

Simplify the above equation,

[tex]{v^2} = \dfrac{{g{{\left( {{s_x}} \right)}^2}}}{{2{{\cos }^2}\theta\cdot \left( {{s_x}\tan \theta- {s_y}} \right)}}[/tex]

Taking the square root both the sides in above equation,

[tex]\boxed{v=\sqrt {\frac{{g{{\left( {{s_x}} \right)}^2}}}{{2{{\cos }^2}\theta\cdot \left( {{s_x}\tan \theta- {s_y}} \right)}}} }[/tex]                                                   …… (3)

Calculation:

Substitute the value of [tex]{s_x}[/tex] as [tex]3.16{\text{ m}}[/tex] , the value of [tex]{s_y}[/tex] as [tex]0.379{\text{ m}}[/tex] , the value of [tex]\theta[/tex]  as [tex]37.6^\circ[/tex]  in equation (3).

[tex]\begin{aligned}v&=\sqrt {\frac{{9.8{{\left( {3.16} \right)}^2}}}{{2{{\cos }^2}37.6^\circ\cdot\left( {3.16\tan 37.6^\circ- 0.379} \right)}}}\\&=\sqrt {\frac{{97.86}}{{2.579}}}\\&=\sqrt {37.945}\\&=6.16{\text{ }}{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {\text{s}}}} \right.\kern-\nulldelimiterspace}{\text{s}}}\\\end{aligned}[/tex]  

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Answer detail:

Grade: Senior School

Subject: Physics

Chapter: Projectile motion

Keywords:

Salmon, jump, waterfall, angle of inclination, continue upstream, projectile, acceleration, velocity, acceleration due to gravity, Newton’s laws, equation of motion, velocity, component of acceleration.

Answer A

Cars A, B, C, D, and E are moving on tracks from left to right. The lengths of the tracks are the same. Assuming each car started at the beginning of its track, which cars are moving at a constant velocity?

A) A and C  

B) B and D  

C) C and E  

D) D and A

The cars A and C are moving with a constant velocity. The correct option is A.

The diagram attached, is a motion diagram, which marks the positions of an object measured at equal time intervals by means of dots.

If the dots are evenly spaced, it shows that the object is making equal displacements in equal intervals of time, which means that the object has a constant velocity.

In the attached diagram, it can be seen that the dots for the cars A and C are equally spaced, showing that these cars are moving with a constant velocity.

The cars B and D are accelerating, since the space between the dots appears to increase.

The car E is decelerating, as the distance between the dots progressively decreases.

Hence only the cars A and C are moving with constant velocities, with A having a greater velocity than C.

Answer: Option A: The number of trees sampled.

The accuracy can be understood as how close is the measured value to the true value.   The aim is to monitor the population size of the insect pest in a 50 square kilometer. Random trees are selected, and number of eggs and larvae are counted. So, the measured value would be closer to actual value when the number of trees sampled are increased. More the number of trees sampled, less would be the chances of error and the accuracy of the estimate would increase.

Answer:

a.) the number of tress sampled

Hey there!

You cannot cut through steel with a plastic knife. As fun as it sounds, it is not a good idea to try, and 99.9% of the time it would not work.

Hope this helps!

It is impossible to cut through steel with a plastic knife because steel is much harder than plastic, and trying to do so could lead to injury.

Steel is a very hard material that requires special tools to cut through effectively due to its high hardness level. Plastic knives are not capable of cutting through steel because they are not hard or sharp enough to overcome the material's resistance. Therefore, It is virtually impossible to cut through steel with a plastic knife due to the significant difference in hardness between the two materials. The hardness of a material dictates how resistant it is to being scratched or cut. For example, steel used in a pocketknife blade has a hardness value of around 5.5, which is considered sufficient to separate between hard and soft minerals. On the other hand, plastics used for items such as plastic cutting boards or plastic knives are much softer.

B) 7.7 x 10^-5 c, hope it helps

Answer:

Choice B is the answer

Explanation:

Ball leaves the table of height 0.60 m

Initial speed of the ball is in horizontal direction which is 2.4 m/s

Now here we can say that time taken by the ball to hit the ground will be given by kinematics equation in vertical direction

[tex]\Delta y = v_y*t + \frac{1}{2}at^2[/tex]

here in y direction we can say

[tex]\Delta y  = 0.60 m[/tex]

[tex]v_y = 0[/tex]

[tex]a = 9.8 m/s^2[/tex] due to gravity

now from above equation we have

[tex]0.60 = 0 + \frac{1}{2}*9.8*t^2[/tex]

[tex]t = 0.35 s[/tex]

Now in the same time the distance that ball move in horizontal direction is given as

[tex]d = v_x* t[/tex]

given that

[tex]v_x = 2.4 m/s[/tex]

[tex]d = 2.4 * 0.35[/tex]

[tex]d = 0.84 m[/tex]

So it will move a total distance of 0.84 m where it will land

The time required for the pool ball to hit the ground is approximately 0.35 seconds and it would cover a horizontal distance of about 0.84 meters from the edge of the table to the landing location.

Your question involves the physics concept of projectile motion. Here, we can use the concepts of horizontal velocity and vertical displacement to calculate the time it would take the pool ball to hit the ground and the horizontal distance it would cover.

Firstly, solving for the fall time, we use the equation of motion: h = 0.5gt², where h is the height, g is the gravity constant (9.8 m/s²), and t is the time. Given the height h = 0.60m, we find t≈0.35s.

Secondly, to find the horizontal distance (the distance between the table's edge and the ball's landing location), we use the formula d = vt, where d is distance, v is horizontal velocity, and t is time. So, d ≈ 2.4m/s * 0.35s = 0.84m.

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Answer:

3.2

Explanation:

Answer:

Driverless cars will transport people to and from the train station.

Explanation:

the person above is correct

The United Kingdom planning to use driverless cars beginning in 2015 in a way such that Driverless cars will transport people to and from the train station, therefore the correct answer is option C.

An EV stands for an electric vehicle. Electric vehicles (EVs) are autos that are powered totally or partially by electricity.

According to a lot of experts, self-driving cars can be programmed to be safer than human drivers.

These automobiles are able to perceive their surroundings and predict what lies ahead, something that humans are not capable of doing thanks to the sensors and cameras that are directing and monitoring them.

The right response is option C since the United Kingdom plans to employ autonomous automobiles starting in 2015 in a mode that will allow them to carry people to and from the railway station.

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For free fall motion the displacement can be found by graphically as well as by kinematics equation

Here acceleration of object is constant as it fall due to gravity so we can use

[tex]d = v_i * t + \frac{1}{2}at^2[/tex]

here if body starts with zero initial speed then we can say

[tex]d = 0 + \frac{1}{2}*9.8*t^2[/tex]

here we need to find the displacement from t = 0 to t = 6s

so we can say

[tex]d = \frac{1}{2}*9.8*6^2[/tex]

[tex]d = 176.4 m[/tex]

so the displacement will be 176.4 m

in order to find the displacement from the graph of velocity and time we need to find the area under the graph for given time interval that will also give us same displacement for given period of time.

Answer:

+360m

Explanation:

You are missing some parts of the question but I have found them else where. The graph will be shown below.

The formula for this is [ d = vt ] where v = velocity and t = time.

On the graph, we can see that the acceleration is constant. The line goes to a maximum velocity of 60m/s and a maximum time of 6 seconds.

Find the displacement with what we are given.

d = 60 * 6

d = 360m

Since we are going forward, we are going to add a "+" sign in front.

Best of Luck!

id have to say its thunder

E =mc²

   = (5.0-kg)(3 x 10^8 m/s)²

   = (5.0-kg) (9×10^16m²/s²)

   E =4.5×10^17 J

Answer:

Its energy equivalent in Joules is

E = 4.5 × 10^17Joules

Explanation:

The Einstein energy equation is expressed as shown

E = mc² where:

m is the mass of the stone

c is the speed of light

Given:

m = 5.0kg

c = 3 x 10^8 m/s

E = 5×(3 x 10^8)²

E = 5×(9×10^16)

E = 45 × 10^16

E = 4.5 × 10^17Joules

OH. I just answered this question yesterday too! E: electrons

Why by Mimiwhatsup: When a atom gains or loses an electron, it will attain a net charge and become an ion.

hey again :)

answer: neutrons

why?: neutrons have a negative charge with a mass of - 1 amu. but trust me it's C.

hope this helps! ❤ from peachimin

When object falls freely we can say

its initial speed will be ZERO

and its acceleration due to gravity must be

[tex]a = g = 9.8 m/s^2[/tex]

Now we need to find the distance of free fall in 3 s of time

So here we will use kinematics

[tex]y = v* t + \frac{1}{2} at^2[/tex]

now we will plug in all values in it

[tex]y = 0 + \frac{1}{2}* 9.8 * 3^2[/tex]

[tex]y = 44.1 m[/tex]

So it will fall by total distance of 44.1 m

Answer:

The brick will cover a distance of [tex]44.1\;\rm{m[/tex].

Explanation:

Given: A brick starting from rest fall freely in 3 seconds.

As mentioned in question,

When an object falls freely then its initial speed will be [tex](u)=0\; \rm{m/s[/tex].

Acceleration due to gravity is [tex]a=g=9.8\;\rm{m/s^{-2[/tex].

Time [tex](t)=3\; \rm{seconds[/tex]

Using the laws of motion: [tex]s=ut+\frac{1}{2}at^2[/tex]

Substiuting all the values we get:

[tex]s=0\times3+\frac{1}{2}\times9.8\times3^2\\s=0.5\times9.8\times 9\\s=44.1\;\rm{m[/tex]

Therefore, the brick will cover a distance of [tex]44.1\;\rm{m[/tex].

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Answer: C)Acceleration due to gravity affects all bodies the same since it depends primarily on the gravity of the planet, not on the object being dropped.

Explanation:

Using equation of motion,

[tex]v^{2}=u^{2}+2gh[/tex]

where v= final velocity , u= initial velocity , h= height from where object is dropped ,acceleration due to gravity , [tex]g=\frac{GM}{R^{2}}[/tex]

G= universal gravitational constant, M=mass of planet , R= radius of planet

Therefore g depends on mass and radius of planet .

=>If all objects are dropped from same height with zero initial speed the final speed depends only on acceleration due to gravity which is a property of planet taken into consideration and does not depend on the object.

For example if a piece of paper and a heavy stone are dropped from the same height with zero initial speed then both objects will have same final speed .

Acceleration due to gravity affects all bodies the same since it depends primarily on the gravity of the planet, not on the object being dropped.

The correct answer is C) Acceleration due to gravity affects all bodies the same since it depends primarily on the gravity of the planet, not on the object being dropped.

Acceleration due to gravity is constant for all objects near the surface of the Earth, regardless of their mass. This means that when objects are dropped from the same height, they will all experience the same acceleration. As a result, they will all hit the ground with the same velocity, disregarding air resistance.

For example, if you drop a feather and a rock from the same height, both will fall at the same rate due to gravity. However, the feather will experience more air resistance and take longer to reach the ground.

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Given

initial position = Xi= 19.9m

Final position Xf = 5.4m

Average velocity= Va = -0.418m/s

it shows displacement is reverse.

To find  t=?

As   Va = (Xf- Xi) / t

t = (Xf-Xi) / ( Va)

t = ( 5.4-19.9) / (-0.418)

t = (-14.5 ) / (-0.418)   (-ve sign cancel out at numerator and denominator)

t =34.69 s

Explanation:

The data given is as follows.

     mass = 2.0 kg

     time = 3 seconds

 gravitational acceleration = [tex]9.8 m/s^{2}[/tex]

Calculate the distance traveled by the rock when it falls is as follows.

          [tex]Distance = \frac{1}{2} \times acceleration \times time^{2}[/tex]

                                 = [tex]\frac{1}{2} \times 9.8 m/s^{2} \times (3 second)^{2}[/tex]

                                 = [tex]\frac{1}{2} \times 9.8 m/s^{2} \times 9 second^{2}[/tex]

                                 = 44.1 m

Therefore, the distance traveled by rock is 44.1 meter.

Answer:yess the correct answer is A

Explanation:

Experimenting to determine the fundamental properties of x-rays would be an example of basic research. The experimental primary analysis tries to determine the laws of the events. The primary analysis is expected to know the stuff, its sort, its characteristics and its performance. It examines to get the speculation. To obtain wherewith the stuff performance yet not how to practice these forms for a firm determination.

The research of the characteristics of the particle to explain whatever it is, how it combines with other atoms, how it determines the characteristics of the material are some instances of primary analysis. For example examining to ascertain the basic features of x-rays. Spencer's research on WWII radar technology that drove to the discovery of the microwave furnace.

Edison's research and application of other scientists task is to create the light bulb, and Morrison and Franscioni's research was made to build the Frisbee models of applied research science.  

Basic research is driven by scientific curiosity, with the aim to enhance the understanding of fundamental principles. In the given choices, B) Experimenting to determine the fundamental properties of x-rays is an example of basic research, as it is looking to better understand these electromagnetic waves.

Basic research, also known as fundamental research or pure research, is designed to extend the knowledge base without a specific application in mind. It is driven by curiosity or interest in a scientific question. The aim is to increase understanding of fundamental principles and has the potential to lead to new inventions or technologies. In the given choices, an example of basic research would be B) Experimenting to determine the fundamental properties of x-rays. This study seeks basic understanding about the nature and properties of these electromagnetic waves, which is the very essence of basic research.

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C

the unit of electric current is the ampere, often shortened to amp

Answer:

A) 33-newton force pointing upward

Explanation:

Hope this help!

0 kg m/s

Momentum is a force that a thing has when it is moving which means when an object is moving only then it will have a non-zero momentum. If an object is stationary, then its momentum is zero.

Formula to calculate the momentum of a moving object multiply the mass of the object times it's velocity.

Momentum = 0 m/s * 4000kg

Momentum = 0 kg m/s

The symbol for momentum is a small p.

The momentum is defined as the product of mass and the velocity of the body. The momentum of the truck will be zero.

The momentum is defined as the product of mass and the velocity of the body. It is denoted by the letter p. It occurs due to the applied force. Its unit is Kg m/s².

The given data in the problem is;

v is the velocity of truck = not given

m is the mass of truck=4000 Kg

p is the momentum of the truck=?

We can not calculate the momentum of the body at rest. Because the momentum of the body at the rest will be zero.

Hence the momentum of the truck will be zero.

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Answer:

18.6 m/s

Explanation:

The frictional force acting on the car is given by:

[tex]F_f = \mu m g=(0.40 )(1200 kg)(9.81 m/s^2)=4709 N[/tex]

But the frictional force also corresponds to the centripetal force that keeps the car in circular motion in the turn:

[tex]F_f = F_c = m \frac{v^2}{r}[/tex]

Where v is the maximum speed the car can achieve remaining in the turn. Substituting r=88.0 m and re-arranging the formula, we can find the value of v:

[tex]v=\sqrt{\frac{Fr}{m}}=\sqrt{\frac{(4709 N)(88.0 m)}{1200 kg}}=18.6 m/s[/tex]

The maximum speed a 1200kg car can round a turn of radius 88m on a flat road given a friction coefficient of 0.40, is around 18.7m/s. This considers the principles of centripetal force and static friction with the assumption of an ideal case scenario.

This problem is a physics scenario that involves centripetal force and static friction. The maximum speed can be calculated using the formula for the centripetal force (F), which in this case is provided by the static friction: F = μN, where μ is the friction coefficient and N is the normal force. In a situation where a car is rounding a turn on a flat road, the normal force N equals to the weight of the car, which is mass (m) times gravity (g). Thus, the equation F = μmg can be used to solve for the centripetal force. The centripetal force equation on the other hand is F = mv² / r, where m is the mass of the car, v is the speed of the car, and r is the radius of the turn. Equating these two equations gives μmg = mv² / r. The mass cancels out resulting to v = sqrt(μgr). Substituting the given values results to maximum speed, v, which is around 18.7 m/s.

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c is the correct answer

it would be 4 kilomotors

A timeline is necessary a. For every goal.

Here are a few reasons why it is so:

The conversions are as follows

60.°C = 333 Kelvin

212 F = 373 K

200 C = 273 K

27 C = 300 K

This question involves matching temperatures in differing scales: degrees Celsius, Kelvin, and Fahrenheit. However, only the first match (60°C to 333K) can be made with the given options. The remaining options don't correspond correctly.

The question involves converting and matching different temperature scales, namely degrees Celsius (°C), Kelvin (K), and degrees Fahrenheit (°F). Here are the matched equivalent temperatures:

The question involves converting and matching different temperature scales, namely degrees Celsius (°C), Kelvin (K), and degrees Fahrenheit (°F). Here are the matched equivalent temperatures:

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The correct answer is water vapor.

Answer: Water Vapor

Explanation:

Kinetic energy is the energy possessed by an object by virtue of its motion.

Solid state : In this state, the molecules are arranged in regular and repeating pattern. The molecules are closely packed that means they are fixed and have low kinetic energy.

For example : Ice

Liquid state : In this state, the molecules are present in random and irregular pattern. The molecules are closely packed but they can move from one place to another and hence have low kinetic energy.

For example : water

Gaseous state : In this state, the molecules are present in irregular pattern. The molecules are not closely packed and they can move freely from one place to another and spread out and thus have high kinetic energy.

For example : water vapor

heat and pressure would be your answer hope it helps

Answer:

heat and pressure

Explanation:

The charge will most likely leave the electric field near C) Y

Answer:

Option (C)

Explanation:

The direction of electric field is upwards

The charge is negative is nature, so the force on the charge particle is in the opposite direction of electric field that means the force on the charged particle is downward. The relation between the force and the electric field is given by

F =  -q x E

So, the charged particle experience a force in the downward direction and then leaves the electric filed near point Y.

Velocity = 1.32

Direction = South

Answer:

Velocity = 0.55 m/s

Direction  = South

Explanation:

Given

let us take the south as positive direction

Velocity of the balloon [tex]v_{b}[/tex] = + 0.87 m/s

Velocity of wind [tex]v_{w}[/tex] = - 0.32 m/s

Solution

Resultant velocity

[tex]v = v_{b} + v_{w} \\\\v = 0.87+(-0.32)\\\\v = 0.55 m/s[/tex]

since the resultant velocity is positive, balloon is directed southward