Chapter 4, Problem 17Q

To determine

The one who has greater final speed.

Answer to Problem 17Q

Solution:

Daughter has greater final speed.

Explanation of Solution

As the daughter and father are pushing each other in the opposite direction, so the horizontal force acting on the father equals to the daughter. Thus, by using Newton’s third law of motion, they exert equal and opposite horizontal force as there is no external force acting on the father and the daughter.

By the conservation of the momentum, the father and daughter have equal momentum as given below:

  $P_{\text{daughter}}=P_{\text{father}}$

The momentum is a product of the mass of an object and its speed, so the mass is inversely proportional to the speed as given below:

  $\begin{array}{l}P=mv\\ m\propto \frac{1}{v}\end{array}$

As the mass of the daughter is less than that of her father, so the speed of the daughter is greater than her father.

Conclusion:

Because the mass of the daughter is less than her father, so she will acquire a greater final speed.