# A 7.0 kg bowling ball moves at 2.50 m / s. How fast must a 2.60 g Ping-Pong ball move so that the...

## Question:

A {eq}7.0 \ kg {/eq} bowling ball moves at {eq}2.50 \ m / s {/eq}. How fast must a {eq}2.60 \ g {/eq} Ping-Pong ball move so that the two balls have the same kinetic energy?

## Kinetic Energy:

Kinetic energy is a form of energy that exists by the virtue of the motion of an object. It is defined as the amount of energy required to set an object in motion from an initial state of rest.

Its value depends on two parameters:

1. The mass of the object.
2. The velocity of the object.

We are given:

• The mass of the bowling ball, {eq}m=7.0\;\rm kg {/eq}
• The velocity of the ball, {eq}v=2.50\;\rm m/s {/eq}
• The mass of the ping-pong ball, {eq}m'=2.60\;\rm g=2.60\times 10^{-3}\;\rm kg {/eq}

Let the velocity of the ping-pong ball be {eq}v' {/eq}

The kinetic energy of an object with mass, {eq}m {/eq}, moving with velocity, {eq}v {/eq}, is given by the equation:

{eq}K=\dfrac{1}{2}mv^2 {/eq}

If the two objects have the same kinetic energy, then we have:

{eq}\begin{align*} \dfrac{1}{2}mv^2&=\dfrac{1}{2}m'v'^2\\ \Rightarrow v'&=v\sqrt{\dfrac{m}{m'}}\\ &=2.50\;\rm m/s\times \sqrt{\dfrac{7.0\;\rm kg}{2.60\times 10^{-3}\;\rm kg}}\\ &=\boxed{1.3\times 10^{2}\;\rm m/s} \end{align*} {/eq}