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

ANSWER

$11.30\text{ m/s}$

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:

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

That is the final velocity of the bowling ball.