Calculate the power output in watts and horsepower of a shot-putter who takes 1.30 s to accelerate the 7.27-kg shot from rest to 16.0 m/s, while raising it 0.900 m. (Do not include the power produced to accelerate his body.) Shot putter at the Dornoch Highland Gathering in 2007.

Answer:

The kinetic energy of an electron is [tex]1.54\times10^{-15}\ J[/tex]

Explanation:

Given that,

Distance = 0.1 nm

We need to calculate the momentum

Using uncertainty principle

[tex]\Delta x\Delta p\geq\dfrac{h}{4\pi}[/tex]

[tex]\Delta p\geq\dfrac{h}{\Delta x\times 4\pi}[/tex]

Where, [tex]\Delta p[/tex] = change in momentum

[tex]\Delta x[/tex] = change in position

Put the value into the formula

[tex]\Delta p=\dfrac{6.6\times10^{-34}}{4\pi\times10^{-10}}[/tex]

[tex]\Delta p=5.3\times10^{-23}[/tex]

We need to calculate the kinetic energy for an electron

[tex]K.E=\dfrac{p^2}{2m}[/tex]

Where, P = momentum

m = mass of electron

Put the value into the formula

[tex]K.E=\dfrac{(5.3\times10^{-23})^2}{2\times9.1\times10^{-31}}[/tex]

[tex]K.E=1.54\times10^{-15}\ J[/tex]

Hence, The kinetic energy of an electron is [tex]1.54\times10^{-15}\ J[/tex]

Answer:

3kg

Explanation:

impulse = MV

then

m1v1=m2v2

when the values are subtitude

then

m2=1.2*25/10

m2=30kg//

Answer:

(i) false

(ii) true

(iii) true

(iv) false

Explanation:

(i) The ratio of Cp and Cv is not constant for all the gases. It is because the value of cp and Cv is different for monoatomic, diatomic and polyatomic gases.

So, this is false.

(ii) For monoatomic gas

Cp = 5R/2, Cv = 3R/2

So, thier ratio

Cp / Cv = 5 / 3 = 1.67

This statement is true.

(iii) for diatomic gases

Cp = 7R/2, Cv = 5R/2

Cp / Cv = 7 / 5 = 1.4

This statement is true.

(iv) It is false.

Answer:

Electric charge, Q = 55.69 C

Explanation:

It is given that,

Electric current drawn by the compressor, I = 23.7 A

Time taken, t = 2.35 s

We need to find the electric charge passes through the circuit during this period. The definition of electric current is given by total charge divided by total time taken.

[tex]I=\dfrac{q}{t}[/tex]

Where,

q is the electric charge

[tex]q=I\times t[/tex]

[tex]q=23.7\ A\times 2.35\ s[/tex]

q = 55.69 C

So, the electric charge passes through the circuit during this period is 55.69 C. Hence, this is the required solution.

Answer:

T = 2.5 lb

N= -0.33 lb

Explanation:

given

r = 9 in

[tex]\dot{r} =-3.6 in/s and\ \ddot{r} = 0[/tex]

[tex]\dot{\theta} = 6.3\ rad/s and\ \ddot{\theta} = 2.1\ rad/s^2[/tex]

[tex]-T = m a_r = m(\ddot{r} -r{\dot{\theta}^2)[/tex]

[tex]N= m a_{\theta} = m(r\ddot{\theta}+2\dot{r}\dot{\theta}})[/tex]

[tex]T= mr{\dot{\theta}^2 = \frac{3}{386.4}(9)(6)^2 =2.5lb[/tex]

[tex]N= m(r\ddot{\theta}+2\dot{r}\dot{\theta}})=\frac{3}{386.4}[9(-2)+2(-2)(6)]=-0.326 lb[/tex]

Answer:

[tex]\frac{dr}{dt} = 0.14 in/s[/tex]

Explanation:

As the volume of the cylinder is constant here so we can say that its rate of change in volume must be zero

so here we can say

[tex]\frac{dV}{dt} = 0[/tex]

now we have

[tex]V = \pi r^2 h[/tex]

now find its rate of change in volume with respect to time

[tex]\frac{dV}{dt} = 2\pi rh\frac{dr}{dt} + \pi r^2\frac{dh}{dt}[/tex]

now we know that

[tex]\frac{dV}{dt} = 0 = \pi r(2h \frac{dr}{dt} + r\frac{dh}{dt})[/tex]

given that

h = 5 inch

r = 2 inch

[tex]\frac{dh}{dt} = - 0.7 in/s[/tex]

now we have

[tex]0 = 2(5) \frac{dr}{dt} + 2(-0.7)[/tex]

[tex]\frac{dr}{dt} = 0.14 in/s[/tex]

Final answer:

The change in radius δr/δt of a cylinder with a constant volume is found to be 0.28 inches per second when the height is decreasing at 0.7 inches per second and r = 2 inches, h = 5 inches.

Explanation:

The question involves using calculus to find the rate of change of the radius of a cylinder given a constant volume and a known rate of change in height. The rate of change of volume for a cylinder, which is 0 because the volume doesn't change, can be described as δV/δt = (πr²) (δh/δt) + (2πrh) (δr/δt) = 0. Given the height is decreasing at 0.7 in/sec, we can find the rate of change of the radius δr/δt. Using the known values of r = 2 inches and h = 5 inches, we can solve for δr/δt.

Starting with the equation for the volume of a cylinder V = πr²h, since the volume is constant, we take the derivative with respect to time to obtain 0 = π(2×r×δr/δt×h + r²×δh/δt). Substituting the known values gives 0 = π(2×2×δr/δt×5 + 2²×(-0.7)), which simplifies to 0 = 20πδr/δt - 5.6π. From this we can solve for δr/δt = 5.6π / 20π = 0.28 in/sec.

The rate of change of the radius is 0.28 inches per second when the height is decreasing at 0.7 inches per second, and the radius is 2 inches while the height is 5 inches.

Answer:

Height of tree = 78.35 meters.

Explanation:

We have

          1 meter = 3.28 feet

That is

          [tex]1 ft = \frac{1}{3.28}=0.3048m[/tex]

Here height of tree = 257 ft

Height of tree = 257 x 0.3048 = 78.35 m

Height of tree = 78.35 meters.

Answer:

The electric field between the plates is 120 V/m.

(c) is correct option.

Explanation:

Given that,

Potential difference = 12 volt

Distance = 10 cm = 0.1 m

We need to calculate the electric field between the plates

Using formula of electric field

[tex]E = \dfrac{V}{d}[/tex]

Where, V = potential difference

d = distance between the plates

Put the formula

[tex]E =\dfrac{12}{0.1}[/tex]

[tex]E=120\ V/m[/tex]

Hence, The electric field between the plates is 120 V/m.

Answer:

h = 3.10 m

Explanation:

As we know that after each bounce it will lose its 11% of energy

So remaining energy after each bounce is 89%

so let say its initial energy is E

so after first bounce the energy is

[tex]E_1 = 0.89 E[/tex]

after 2nd bounce the energy is

[tex]E_2 = 0.89(0.89 E)[/tex]

After third bounce the energy is

[tex]E_3 = (0.89)(0.89)(0.89)E[/tex]

here initial energy is given as

[tex]E = mgH_o[/tex]

now let say final height is "h" so after third bounce the energy is given as

[tex]E_3 = mgh[/tex]

now from above equation we have

[tex]mgh = (0.89)(0.89)(0.89)(mgH)[/tex]

[tex]h = 0.705H[/tex]

[tex]h = 0.705(4.4 m)[/tex]

[tex]h = 3.10 m[/tex]

Answer:

Driving speed of the car = 10 m/s

Explanation:

The car hits the water a distance of 15 meters from the base of the cliff.

Horizontal displacement = 11 m

A robot car drives off a cliff that is 11 meters above the water below.

Vertical displacement = 11 m

We have

     s = ut + 0.5 at²

     11 = 0 x t + 0.5 x 9.81 x t²

      t = 1.50 s

So the car moves 15 meters in 1.50 seconds.

     Velocity

             [tex]v=\frac{15}{1.5}=10m/s[/tex]

Driving speed of the car = 10 m/s

Answer:

The magnitude of the magnetic field inside the solenoid is [tex]7.3\times10^{-3}\ T[/tex].

Explanation:

Given that,

Length = 81.0 cm

Radius = 1.70 cm

Number of turns = 1300

Current = 3.60 A

We need to calculate the magnetic field

Using formula of magnetic field inside the solenoid

[tex]B =\mu nI[/tex]

[tex]B =\mu\dfrac{N}{l}I[/tex]

Where, [tex]\dfrac{N}{l}[/tex]=Number of turns per unit length

I = current

B = magnetic field

Put the value into the formula

[tex]B =4\pi\times10^{-7}\times\dfrac{1300}{81.0\times10^{-2}}\times3.60[/tex]

[tex]B = 7.3\times10^{-3}\ T[/tex]

Hence, The magnitude of the magnetic field inside the solenoid is [tex]7.3\times10^{-3}\ T[/tex].

Answer: 2561.7 pounds

Explanation:

If we assume the total weight of an airplane (in pounds units) as a linear function of the amount of fuel in its tank (in gallons) and we make a Weight vs amount of fuel graph, which resulting slope is 5.7, we can use the slope equation of the line:

[tex]m=\frac{Y-Y_{1}}{X-X_{1}}[/tex]  (1)

Where:

[tex]m=5.7[/tex] is the slope of the line

[tex]Y_{1}=2390.7pounds[/tex] is the airplane weight with  51 gallons of fuel in its tank (assuming we chose the Y axis for the airplane weight in the graph)

[tex]X_{1}=51gallons[/tex] is the fuel in airplane's tank for a total weigth of 2390.7 pounds (assuming we chose the X axis for the a,ount of fuel in the tank in the graph)

This means we already have one point of the graph, which coordinate is:

[tex](X_{1},Y_{1})=(51,2390.7)[/tex]

Rewritting (1):

[tex]Y=m(X-X_{1})+Y_{1}[/tex]  (2)

As Y is a function of X:

[tex]Y=f_{(X)}=m(X-X_{1})+Y_{1}[/tex]  (3)

Substituting the known values:

[tex]f_{(X)}=5.7(X-51)+2390.7[/tex]  (4)

[tex]f_{(X)}=5.7X-290.7+2390.7[/tex]  (5)

[tex]f_{(X)}=5.7X+2100[/tex]  (6)

Now, evaluating this function when X=81 (talking about the 81 gallons of fuel in the tank):

[tex]f_{(81)}=5.7(81)+2100[/tex]  (7)

[tex]f_{(81)}=2561.7[/tex]  (8)   This means the weight of the plane when it has 81 gallons of fuel in its tank is 2561.7 pounds.

Final answer:

To find the weight of the airplane with 81 gallons of fuel, calculate the additional fuel weight (30 gallons
* 5.7 pounds/gallon = 171 pounds) and add it to the initial weight (2390.7 pounds + 171 pounds = 2561.7 pounds).

Explanation:

The question asks to calculate the weight of an airplane with a different amount of fuel in its tank, given the weight with a specific amount and the slope of weight increase per gallon of fuel added. To find the new weight, we first calculate the weight increase due to the additional fuel, then add this increase to the original weight of the airplane.

Initial weight with 51 gallons: 2390.7 pounds
Fuel increase: 81 gallons - 51 gallons = 30 gallons
Slope (rate of weight increase): 5.7 pounds per gallon
Additional weight from extra fuel: 30 gallons
* 5.7 pounds/gallon = 171 pounds
New weight with 81 gallons: 2390.7 pounds + 171 pounds = 2561.7 pounds

Answer:

Final temperature = 52.44 °C

Explanation:

We have equation for thermal expansion

        ΔL = LαΔT

We have change in length = Circumference of 2.35 cm radius - Circumference of 2.34 cm radius = 2π x 2.35 - 2π x 2.34 = 0.062 cm

Length of eyeglass frame = 2π x 2.34 = 14.70 cm

Coefficient of linear expansion, α = 1.30 x 10⁻⁴ °C⁻¹

Substituting

        0.062 = 14.70 x 1.30 x 10⁻⁴ x ΔT    

         ΔT = 32.44°C

         Final temperature = 32.44 + 20 = 52.44  °C

To fit lenses of 2.35 cm radius into eyeglass frames with lens holes of 2.34 cm radius at room temperature, the frames made of an epoxy plastic should be heated to about 52°C. This fact is obtained using the physics concept of thermal expansion.

The question relates to the concept of thermal expansion typically studied in physics. The change in radius due to thermal expansion in a one-dimensional system like the eyeglass frames can be given by the formula Δr = αr(ΔT), where Δr is the change in radius, α is the coefficient of expansion, r is the initial radius, and ΔT is the change in temperature. Upon heating, the frames will expand and their lens holes will become larger. Here, we are trying to determine the temperature needed to increase the hole radius from 2.34 cm to 2.35 cm. Using the above formula:

0.01 cm = 1.30 × 10−4°C−1 * 2.34 cm * ΔT

Solving for ΔT (the change in temperature), we get ΔT = about 32°C. Thus, the frames need to be heated to about 32°C above room temperature, i.e., 20°C + 32°C = 52°C.

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Answer:

C. 150 N to the left

Explanation:

If we take right to be positive and left to be negative, then:

∑F = -450 N + 300 N

∑F = -150 N

The net force is 150 N to the left.

Answer:

(C) 150 N to the left

Explanation:

It is given that,

Force acting in left side, F = 450 N

Force acting in right side, F' = 300 N

Let left side is taken to be negative while right side is taken to be positive. So,

F = -450 N

F' = +300 N

The net force will act in the direction where the magnitude of force is maximum. Net force is given by :

[tex]F_{net}=-450\ N+300\ N[/tex]

[tex]F_{net}=-150\ N[/tex]    

So, the net force on the table is 150 N and it is acting to the left side. Hence, the correct option is (c).

Answer:

Common trade name of polytetrafluoroethylene is Teflon

Many uses are there some of them are given in explanation.

Explanation:

Common trade name of polytetrafluoroethylene is Teflon.

Main uses of polytetrafluoroethylene:

1) To coat non stick pans

2) Used as ski bindings

3)  Used as fabric protector to repel stains on formal school-wear

4) Used to make to make a waterproof, breathable fabric in outdoor apparel.

In this situation, the neon gas should also have a temperature of 175 K, the same as the helium gas, given all the conditions and the principle of the ideal gas law.

The problem you're working on involves understanding the ideal gas law, which is PV = nRT. This equates the pressure (P), volume (V) of the gas, and temperature (T). There are two important points to consider. Firstly, the number of molecules or moles (n) and the ideal gas constant (R) aren't changing in this situation. Secondly, the volume and pressure are the same for both gases.

Given that the masses, volume, and pressure are the same for both helium and neon, we conclude that the number of moles (n) for helium and neon are equal (because the mass density is the same and for ideal gas mass density (ρ) = PM/RT, where M is molar mass). The temperature ratio should be the same as the ratio of Kelvin temperatures of two gases.

So, we can safely say that since the gases obey the ideal gas law, and all conditions are held constant aside from the identity of the gas and the temperature, the temperature of the neon gas must also be 175 Kelvin like the helium gas.

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Answer:

alternative E- none of these answers

Explanation:

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity. Hydrostatic pressure increases in proportion to depth measured from the surface because of the increasing weight of fluid exerting downward force from above.

The formula is :

P= d x g x h

p: hydrostatic pressure (N/m²)

d: density (kg/m³) density of seawater is 1,030 kg/m³

g: gravity (m/s²) ≅ 9.8m/s²

h: height (m)

The hydrostatic pressure at 20,000 leagues under the sea is approximately 1,002,500,000,000 Pa.

The hydrostatic pressure at 20,000 leagues under the sea can be calculated using the equation for pressure in a fluid, which is given by P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth below the surface.

Since a league is the distance a person can walk in one hour, we need to convert it to meters. Assuming an average walking speed of 5 km/h, a league is equal to 5 km. Therefore, 20,000 leagues is equal to 100,000 km.

The pressure at this depth can be calculated using the known values: density of seawater is about 1025 kg/m³ and acceleration due to gravity is 9.8 m/s². Plugging in these values, we get P = (1025 kg/m³)(9.8 m/s²)(100,000,000 m) = 1,002,500,000,000 Pa.

Therefore, the correct answer is none of the provided options. The hydrostatic pressure at 20,000 leagues under the sea is approximately 1,002,500,000,000 Pa.

Answer:

Part a)

A = 66.2 m

Part b)

Angle = 38.35 degree

Explanation:

Part a)

Length of the vector is the magnitude of the vector

here we know that

[tex]A_x = 52.0 m[/tex]

[tex]A_y = 41.0 m[/tex]

now we have

[tex]A = \sqrt{A_x^2 + A_y^2}[/tex]

[tex]A = \sqrt{52^2 + 41^2}[/tex]

[tex]A = 66.2 m[/tex]

Part b)

Angle made by the vector is given as

[tex]tan\theta = \frac{A_y}{A_x}[/tex]

[tex]tan\theta = \frac{41}{52}[/tex]

[tex]\theta = 38.25 degree[/tex]

Answer:

a)  Final velocity of the dragster at the end of 1.8 s = 75.6 m/s

b) Final velocity of the dragster at the end of 3.6 s = 151.2 m/s

c) The displacement of the dragster at the end of 1.8 s = 68.04 m

d) The displacement of the dragster at the end of 3.6 s = 272.16 m

Explanation:

a) We have equation of motion v = u + at

  Initial velocity, u =  0 m/s

 Acceleration , a = 42 m/s²

 Time = 1.8 s    

Substituting

  v = u + at

  v  = 0 + 42 x 1.8 = 75.6 m/s

Final velocity of the dragster at the end of 1.8 s = 75.6 m/s

b) We have equation of motion v = u + at

  Initial velocity, u =  0 m/s

 Acceleration , a = 42 m/s²

 Time = 3.6 s    

Substituting

  v = u + at

  v  = 0 + 42 x 3.6 = 75.6 m/s

Final velocity of the dragster at the end of 3.6 s = 151.2 m/s

c) We have equation of motion s= ut + 0.5 at²

  Initial velocity, u =  0 m/s

 Acceleration , a = 42 m/s²

 Time = 1.8 s    

Substituting

   s= ut + 0.5 at²

    s = 0 x 1.8 + 0.5 x 42 x 1.8²

    s = 68.04 m

The displacement of the dragster at the end of 1.8 s = 68.04 m

d) We have equation of motion s= ut + 0.5 at²

  Initial velocity, u =  0 m/s

 Acceleration , a = 42 m/s²

 Time = 3.6 s    

Substituting

   s= ut + 0.5 at²

    s = 0 x 3.6 + 0.5 x 42 x 3.6²

    s = 272.16 m

The displacement of the dragster at the end of 3.6 s = 272.16 m

Answer:

49.07 miles

Explanation:

Angle between two ships = 110° = θ

First ship speed = 22 mph

Second ship speed = 34 mph

Distance covered by first ship after 1.2 hours = 22×1.2 = 26.4 miles = b

Distance covered by second ship after 1.2 hours = 34×1.2 = 40.8 miles = c

Here the angle between the two sides of a triangle is 110° so from the law of cosines we get

a² = b²+c²-2bc cosθ

⇒a² = 26.4²+40.8²-2×26.4×40.8 cos110

⇒a² = 2408.4

⇒a = 49.07 miles

1) Time: 2 s, 6 s

The position of the particle is given by:

[tex]x=t^3 -12t^2 +36t+32[/tex]

where t is the time in seconds and x is the position in feet.

The velocity of the particle can be found by differentiating the position:

[tex]v(t)=x'(t)=3t^2 -24t+36[/tex]

and it is expressed in ft/s.

In order to find the time at which the velocity is v=0 ft/s, we substitute v=0 into the previous equation:

[tex]0=3t^2-24t+36\\0=t^2 -8t+12\\0=(t-2)(t-6)[/tex]

So the two solutions are

t = 2 s

t = 6 s

2) Position: x = 64 ft and x = 32 ft

The position at which the velocity of the particle is v = 0 can be found by susbtituting t = 2 and t = 6 into the equation for the position.

For t = 2 s, we have

[tex]x=(2)^3-12(2)^2 +36(2)+32=64[/tex]

For t = 6 s, we have

[tex]x=(6)^3-12(6)^2 +36(6)+32=32[/tex]

So the two positions are

x = 64 ft

x = 32 ft

3) Acceleration: [tex]-12 ft/s^2[/tex] and [tex]+12 ft/s^2[/tex]

The acceleration of the particle can be found by differentiating the velocity. We find:

[tex]a(t)=v'(t)=6t-24[/tex]

And substituting t = 2 and t = 6, we find the acceleration when the velocity of the particle is zero:

[tex]a(2)=6(2)-24=-12[/tex]

[tex]a(6)=6(6)-24=12[/tex]

So the two accelerations are

[tex]a=-12 ft/s^2[/tex]

[tex]a=12 ft/s^2[/tex]

The time, position, and acceleration of the particle when v = 0 ft/s are t = 2 s and t = 6 s, x = 24 ft and x = 184 ft, and a = -12 ft/s² and a = 12 ft/s².

To find the time, position, and acceleration of the particle when the velocity is 0 ft/s, we need to determine the values of t, x, and a when v = 0.

Given the relation x = t³ - 12t² + 36t + 32, we need to solve for t when v = 0. We can use the equation v = dx/dt to find the velocity function and set it equal to 0.

By differentiating x with respect to t, we get v = 3t² - 24t + 36. Setting v = 0, we can solve the quadratic equation 3t² - 24t + 36 = 0 to find the values of t. The solutions are t = 2 and t = 6.

Therefore, when v = 0, the time is t = 2 s and t = 6 s. We can substitute these values into the position function to find the corresponding positions. When t = 2 s, x = (2)³ - 12(2)² + 36(2) + 32 = 24 ft. When t = 6 s, x = (6)³ - 12(6)² + 36(6) + 32 = 184 ft.

To find the acceleration, we can differentiate the velocity function with respect to t. By differentiating v = 3t² - 24t + 36, we get a = 6t - 24. Substituting t = 2 s and t = 6 s into this equation, we get a = 6(2) - 24 = -12 ft/s² and a = 6(6) - 24 = 12 ft/s².

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Answer:

0.28 J

Explanation:

Since the air-hockey puck was initially at rest

KE₀ = initial kinetic energy of the air-hockey puck = 0 J

KE = final kinetic energy of the air-hockey puck

m = mass of air-hockey puck 0.5 kg

F = net force = 0.4 N

d = distance moved = 0.7 m

Using work-change in kinetic energy

F d = (KE - KE₀)

(0.4) (0.7) = KE - 0

KE = 0.28 J

Answer:

The initial temperature of the gas was of T1= 112ºC .

Explanation:

T1= ?

T2= 35 ºC = 308.15 K

V1= 0.225 L

V2= 0.18 L

T2* V1 / V2 = T1

T1= 385.18 K = 112ºC

Answer:

Explanation:

As the dielectric is inserted between the plates of a capacitor, the capacitance becomes K times and the electric field between the plates becomes 1 / K times the original value. Where, K be the dielectric constant.

Answer:

A primitive solid is a 'building block' that you can use to work with in 3D. Rather than extruding or revolving an object, AutoCAD has some basic 3D shape commands at your disposal.

Explanation:

Answer:

a) Total displacement  = 3986.54 m

b) Average speeds

      Leg 1 ->  11.22 m/s

      Leg 2 ->  22.44 m/s

      Leg 3 ->  11.20 m/s

      Complete trip ->  21.63 m/s

Explanation:

a) Leg 1:

Initial velocity, u =  0 m/s

Acceleration , a = 2.04 m/s²

Time, t = 11 s

We have equation of motion s= ut + 0.5 at²

Substituting

   s= ut + 0.5 at²

    s = 0 x 11 + 0.5 x 2.04 x 11²

    s = 123.42 m

Leg 2:

We have equation of motion v = u + at

Initial velocity, u =  0 m/s

Acceleration , a = 2.04 m/s²

Time, t = 11 s

Substituting

   v = 0 + 2.04 x 11 = 22.44 m/s

We have equation of motion s= ut + 0.5 at²

Initial velocity, u =  22.44 m/s

Acceleration , a = 0 m/s²

Time, t = 2.85 min = 171 s

Substituting

   s= ut + 0.5 at²

    s = 22.44 x 171 + 0.5 x 0 x 171²

    s = 3837.24 m

a) Leg 3:

Initial velocity, u =  22.44 m/s

Acceleration , a = -9.73 m/s²

Time, t = 2.31 s

We have equation of motion s= ut + 0.5 at²

Substituting

   s= ut + 0.5 at²

    s = 22.44 x 2.31 + 0.5 x -9.73 x 2.31²

    s = 25.88 m

Total displacement = 123.42 + 3837.24 + 25.88 = 3986.54 m

Average speed is the ratio of distance to time.

b) Leg 1:

        [tex]v_{avg}=\frac{123.42}{11}=11.22m/s[/tex]

 Leg 2:

        [tex]v_{avg}=\frac{3837.24}{171}=22.44m/s[/tex]

Leg 3:

        [tex]v_{avg}=\frac{25.88}{2.31}=11.20m/s[/tex]

Complete trip:

        [tex]v_{avg}=\frac{3986.54}{11+171+2.31}=21.63m/s[/tex]

Answer:

1270.44 Hz

Explanation:

[tex]v_{L}[/tex]  = velocity of the our car = 35.0 m/s

[tex]v_{P}[/tex]  = velocity of the police car = ?

[tex]v_{S}[/tex]  = velocity of the sound = 343 m/s

[tex]f_{app}[/tex]  = frequency observed as police car approach = 1310 Hz

[tex]f_{rec}[/tex]  = frequency observed as police car go away = 1240 Hz

[tex]f[/tex]  = actual frequency of police siren

Frequency observed as police car approach is given as

[tex]f_{app}= \frac{(v_{s}-v_{L})f}{v_{s} -v_{P} }[/tex]

inserting the values

[tex]1310 = \frac{(343 - 35)f}{343 -v_{P} }[/tex]                          eq-1

Frequency observed as police car goes away is given as

[tex]f_{rec}= \frac{(v_{s} + v_{L})f}{v_{s} + v_{P} }[/tex]

inserting the values

[tex]1240 = \frac{(343 + 35)f}{343 + v_{P} }[/tex]                          eq-2

Dividing eq-1 by eq-2

[tex]\frac{1310}{1240} = \left ( \frac{343 - 35}{343 - v_{P} } \right )\frac{(343 + v_{P})}{343 + 35 }\\[/tex]

[tex]v_{P}[/tex]  = 44.3 m/s

Using eq-1

[tex]1310 = \frac{(343 - 35)f}{343 - 44.3 }[/tex]

f = 1270.44 Hz

Answer:

Moessbauer Effect = eggy eggs

Explanation:

Answer:

Period of oscillation, T = 2 sec

Explanation:

It is given that,

Mass of the object, m = 5 kg

Spring constant of the spring, k = 50 N/m

This object is hanging from a coiled spring. We need to find the period of oscillation of the spring. The time period of oscillation of the spring is given by :

[tex]T=2\pi\sqrt{\dfrac{m}{k}}[/tex]

[tex]T=2\pi\sqrt{\dfrac{5\ kg}{50\ N/m}}[/tex]

T = 1.98 sec

or

T = 2 sec

So, the period of oscillation is about 2 seconds. Hence, this is the required solution.

Answer:

a) [tex]4.1\times 10^{6} \frac{m}{s}[/tex]

b) [tex]9.2\times 10^{-8} s[/tex]

c) [tex]5.6\times 10^{-14} J[/tex]

d) 175000 volts

Explanation:

a)

[tex]q[/tex]  = magnitude of charge on the alpha particle = 2 x 1.6 x 10⁻¹⁹ C = 3.2 x 10⁻¹⁹ C

[tex]m[/tex]  = mass of alpha particle = 4 x 1.67 x 10⁻²⁷ kg = 6.68 x 10⁻²⁷ kg

[tex]r[/tex]  = radius of circular path = 5.99 cm = 0.0599 m

[tex]B[/tex]  = magnitude of magnetic field = 1.43 T

[tex]v[/tex] = speed of the particle

Radius of circular path is given as

[tex]r = \frac{mv}{qB}[/tex]

[tex]0.0599 = \frac{(6.68\times 10^{-27})v}{(3.2\times 10^{-19})(1.43)}[/tex]

[tex]v = 4.1\times 10^{6} \frac{m}{s}[/tex]

b)

Time period is given as

[tex]T = \frac{2\pi m}{qB}[/tex]

[tex]T = \frac{2(3.14)(6.68\times 10^{-27})}{(3.2\times 10^{-19})(1.43)}[/tex]

[tex]T = 9.2\times 10^{-8} s[/tex]

c)

Kinetic energy is given as

[tex]K = (0.5)mv^{2}[/tex]

[tex]K = (0.5)(6.68\times 10^{-27})(4.1\times 10^{6})^{2}[/tex]

[tex]K = 5.6\times 10^{-14} J[/tex]

d)

ΔV = potential difference

Using conservation of energy

q ΔV = K

(3.2 x 10⁻¹⁹) ΔV = 5.6 x 10⁻¹⁴

ΔV = 175000 volts