Chapter 7, Problem 1QAP

To determine

That will the basketball and tennis ball can have same momentum if mass of basketball is $18$times of a tennis ball.

Explanation of Solution

Given data:

Mass of basketball, $m_{\text{basket}\text{ball}}=18m_{\text{tennis}\text{ball}}$ (mass of tennis ball)

Formula used:

Momentum, $p_x=m{v}_x$

Where m= mass and $v_x$ = velocity in x- direction.

Calculation:

Yes, both can have same momentum.

By utilizing the formula of momentum.

Momentum, $p_x=m{v}_x$

Where m= mass and $v_x$ = velocity in x- direction.

  $\begin{array}{l}{p}_{\text{basket}\text{ball}}=p_{\text{tennis}\text{ball}}\\ \\ m_{\text{basket}\text{ball}}{v}_{\text{basket}\text{ball}}=m_{\text{tennis}\text{ball}}{v}_{\text{tennis}\text{ball}}\\ \\ v_{\text{tennis}\text{ball}}=\frac{m_{\text{basket}\text{ball}}}{m_{\text{tennis}\text{ball}}}{v}_{\text{basket}\text{ball}}=\left(\frac{18m_{\text{tennis}\text{ball}}}{m_{\text{tennis}\text{ball}}}\right)v_{\text{basket}\text{ball}}=18v_{\text{basket}\text{ball}}\end{array}$

Conclusion:

Yes, the basketball having $18$times mass of a tennis ballcan have same momentum as that of tennis ball if the tennis ball moves $18$ times faster than the basketball.