Chapter 5, Problem 9RAT

Standing on a stakeboard, you toss a ball horizontally away from you. The mass of the ball is one-tenth your mass. Compared with the speed you give to the ball, your ideal recoil speed will be

(a) one-tenth as much.

(b) the same

(c) ten times as much

(d) one hundred times as much

To determine

The correct option for the statement, “Standing on a stakeboard, you toss a ball horizontally away from you. The mass of the ball is one-tenth your mass. Compared with the speed you give to the ball, your ideal recoil speed will be”.

Answer to Problem 9RAT

The correct option for the statement, “Standing on a stakeboard, you toss a ball horizontally away from you. The mass of the ball is one-tenth your mass. Compared with the speed you give to the ball, your ideal recoil speed will be” is option (c).

Explanation of Solution

The momentum is a conserved quantity, which means that the momentum of the system before the event will remain the same after the event also if no external force acts over it. The mass of the person is 10 times the mass of the ball.

Consider that the mass of the ball is $m$, mass of the person is $10m$, speed of the ball is $v$, and the recoil speed of the system is $v^{\prime }$.

Write the expression for the law of conservation of momentum.

$\begin{array}{c}m{v}_{\text{before}\text{event}}=m{v}_{\text{after}\text{event}}\\ mv=\left(10m+m\right)v^{\prime }\\ v^{\prime }=\frac{v}{11}\end{array}$

So, the recoil speed of the person after it catches the ball as compared to speed of ball is approximately one-tenth as much.

Conclusion:

Therefore, the correct option for the statement, “Standing on a stakeboard, you toss a ball horizontally away from you. The mass of the ball is one-tenth your mass. Compared with the speed you give to the ball, your ideal recoil speed will be” is option (c).