# How fast (in m/s) must a 2.7-g ping-pong ball move in order to have the same kinetic energy as a...

## Question:

How fast (in m/s) must a 2.7-g ping-pong ball move in order to have the same kinetic energy as a 145 g baseball moving at 35.0 m/s?

## Kinetic Energy:

The kinetic energy of a moving body can be quantified using the equation, {eq}\displaystyle KE = \frac{1}{2}mv^2 {/eq}. In this equation, m is the mass of the moving body while v is its velocity. We can use this equation in certain conditions such as conservation of the momentum or energy of an object.

Determien the velocity of the pingpong ball, {eq}\displaystyle v_1 {/eq}, with a mass of {eq}\displaystyle m_1 = 2.7\ g {/eq}, such that its kinetic energy, {eq}\displaystyle KE = \frac{1}{2}mv^2 {/eq}, is equal to that of a baseball with a velocity of {eq}\displaystyle v_2 = 35.0 \ m/s {/eq} and a mass of {eq}\displaystyle m_2 = 145\ g {/eq}, by equating their kinetic energies, {eq}\displaystyle KE_1 = KE_2 {/eq}. We proceed with the solution.

{eq}\begin{align} \displaystyle KE_1 &= KE_2\\ \frac{1}{2}m_1v_1^2 &= \frac{1}{2}m_2v_2^2\\ v_1^2 &= \frac{m_2}{m_1}v_2^2\\ v_1 &=\sqrt{\frac{m_2}{m_1}v_2^2}\\ &= \sqrt{\frac{145\ g}{2.7\ g}(35.0\ m/s)^2}\\ &\approx \boxed{ \rm 256\ m/s} \end{align} {/eq} 