Question

If a 10.8 kg bowling ball moving at 12 m/s collides with a basketball with mass .58 kg moving in a different direction at 4 m/s. If the ball bounces back at 9 m/s. What is the velocity of the bowling ball?

Answer 1

`11.30\text{ m/s}`

Step-by-step explanation

To find the velocity of the bowling ball, we apply the law of conservation of momentum, which states that the total momentum in a system is constant.

Mathematically, it is written as:

`mu+MU=mv+MV`

where m = mass of bowling ball = 10.8 kg

M = mass of basketball = 0.58 kg

u = initial velocity of bowling ball = 12 m/s

U = initial velocity of basketball = -4 m/s

v = final velocity of bowling ball

V = final velocity of basketball = 9 m/s

Note: the initial velocity of the basketball is negative since it is moving in a different direction from the bowling ball.

We have to solve for final velocity, v.

Therefore, we have:

`\begin{gathered} mu+MU-MV=mv \\ \Rightarrow v=(mu+M(U-V))/(m) \\ v=((10.8\cdot12)+0.58(-4-9))/(10.8) \\ v=(129.6+-7.54)/(10.8) \\ v=(122.06)/(10.8) \\ v=11.30\text{ m/s} \end{gathered}`

That is the final velocity of the bowling ball.