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arsen [322]
3 years ago
10

Physics help please

Physics
1 answer:
zhuklara [117]3 years ago
5 0

Answer: 37.981 m/s

Explanation:

This situation is related to projectile motion or parabolic motion, in which the travel of the ball has two components: <u>x-component</u> and <u>y-component.</u> Being their main equations as follows:

<u>x-component: </u>

x=V_{o}cos\theta t   (1)

Where:

x=52 m is the point where the ball strikes ground horizontally

V_{o} is the ball's initial speed

\theta=0 because we are told the ball is thrown horizontally

t is the time since the ball is thrown until it hits the ground

<u>y-component: </u>

y=y_{o}+V_{o}sin\theta t+\frac{gt^{2}}{2}   (2)

Where:

y_{o}=120m  is the initial height of the ball

y=0  is the final height of the ball (when it finally hits the ground)

g=-9.8m/s^{2}  is the acceleration due gravity

Knowing this, let's start by finding t from (2):

<u></u>

0=y_{o}+V_{o}sin(0\°) t+\frac{gt^{2}}{2}   (3)

0=y_{o}+\frac{gt^{2}}{2}  

t=\sqrt{\frac{-2 y_{o}}{g}}   (4)

t=\sqrt{\frac{-2 (120 m)}{-9.8m/s^{2}}}   (5)

t=4.948 s   (6)

Then, we have to substitute (6) in (1):

x=V_{o}cos(0\°) t   (7)

And find V_{o}:

V_{o}=\frac{x}{t}   (8)

V_{o}=\frac{52 m}{4.948 s}   (9)

V_{o}=10.509 m/s   (10)

On the other hand, since we are dealing with constant acceleration (due gravity) we can use the following equation to find the value of the ball's final velocity V:

V=V_{o} + gt (11)

V=10.509 m/s + (-9.8 m/s^{2})(4.948 s) (12)

V=-37.981 m/s (13) This is the ball's final velocity, and the negative sign indicates its direction is downwards.

However, we were asked to find the <u>ball's final speed</u>, which is the module of the ball's final vleocity vector. This module is always positive, hence the speed of the ball just before it strikes the ground is 37.981 m/s (positive).

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A Ferris wheel on a California pier is 27 m high and rotates once every 32 seconds in the counterclockwise direction. When the w
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So the angular velocity is

\omega=\frac{2\pi}{T}=\frac{2\pi}{32 s}=0.20 rad/s

Assuming the wheel is moving at constant angular velocity, we can now calculate the angular displacement with respect to the initial position:

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and substituting t = 75 seconds, we find

\theta= (0.20 rad/s)(75 s)=15 rad

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15 rad: x = 2\pi rad : 360^{\circ}\\&#10;x=\frac{(15 rad)(360^{\circ})}{2\pi}=860^{\circ} = 140^{\circ}

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v=\omega r

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\omega=0.20 rad/s

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Answer:

a)   v_{f} = 0.25 m / s  b) u = 0.25 m / s

Explanation:

a) To solve this problem let's start with the conservation of the moment, for this we define a system formed by the ball plus the dog, in this case all the forces are internal and the moment is conserved

We will write the data

     m₁ = 0.40 kg

     v₁₀ = 9.0 m / s

     m₂ = 14 kg

     v₂₀ = 0

Initial

     po = m₁ v₁₀

Final

     p_{f} = (m₁ + m₂) vf

     po = pf

     m₁ v₁₀ = (m₁ + m₂) v_{f}

      v_{f} = v₁₀ m₁ / (m₁ + m₂)

      v_{f} = 9.0 (0.40 / (0.40 +14)

      v_{f} = 0.25 m / s

b) This is the reference frame of the center of mass of the system in this case the speed of this frame is the speed of the center of mass

      u = 0.25 m / s

In the direction of movement of the ball

c) Let's calculate the kinetic energy in both moments

Initial

     K₀ = ½ m₁ v₁₀² +0

     K₀ = ½ 0.40 9 2

     K₀ = 16.2 J

Final

     K_{f}= ½ (m₁ + m₂) v_{f}2

      K_{f} = ½ (0.4 +14) 0.25 2

    K_{f} = 0.45 J

   

    ΔK = K₀ -  K_{f}

    ΔK = 16.2-0.445

    ΔK = 1575 J

These will transform internal system energy

d) In order to find the kinetic energy, we must first find the velocities of the individual in this reference system.

      v₁₀’= v₁₀ -u

      v₁₀’= 9 -.025

      v₁₀‘= 8.75 m / s

      v₂₀ ‘= v₂₀ -u

      v₂₀‘= - 0.25 m / s

      v_{f} ‘=   v_{f} - u

      v_{f} = 0

Initial

    K₀ = ½ m₁ v₁₀‘² + ½ m₂ v₂₀‘²

    Ko = ½ 0.4 8.75² + ½ 14.0 0.25²

    Ko = 15.31 + 0.4375

    K o = 15.75 J

Final

   k_{f} = ½ (m₁ + m₂) vf’²

  k_{f} = 0

All initial kinetic energy is transformed into internal energy in this reference system

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3 years ago
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