Chapter 8, Problem 18A

Imagine that you are hovering next to the space shuttle in an Earth orbit. Your buddy of equal mass, who is moving at 4 km/h with respect to the shuttle, bumps into you. If he holds onto you, how fast do you both move with respect to the ship?

To determine

The speed of both the person move with respect to the ship.

Answer to Problem 18A

The speed of both the person move with respect to the ship is $2\text{km}/\text{h}$ .

Explanation of Solution

Given info:

The speed of the person 2 is $v_2=4\text{km}/\text{h}$ .

Formula Used:

Consider the speed of the person 1 who is hovering as $v_1=0$ .

The expression of law of conservation of momentum as follows:

  ${\text{Net momentum}}_{\text{Before bumping}}={\text{Net momentum}}_{\text{After bumping}}$

Calculation:

The speed of both the person move with respect to the ship as follows:

  $\begin{array}{l}{\text{Net momentum}}_{\text{Before bumping}}={\text{Net momentum}}_{\text{After bumping}}\\ m{v}_1+m{v}_2=\left(m+m\right)v\\ F_{\text{net}}=mg\\ m\left(v_1+v_2\right)=2mv\end{array}$

  $\begin{array}{l}{v}_1+v_2=2v\\ \left(0\text{km}/\text{h}\right)+\left(4\text{km}/\text{h}\right)=2v\\ v=2\text{km}/\text{h}\end{array}$

Conclusion:

Thus, the speed of both the person move with respect to the ship is $2\text{km}/\text{h}$ .