Chapter 7, Problem 66GP

To determine

The distance between the two astronauts

Answer to Problem 66GP

28 m.

Explanation of Solution

Given:

Mass of the heavier astronaut $=m_1=60\text{kg}$

Mass of the lighter astronaut $=m_2=80\text{kg}$

Distance moved by lighter astronaut $=d_2=12\text{m}$

Distance moved by heavier astronaut $=d_1$

Distance between the two astronauts $=d$

Formula Used:

In the absence of an external force on the system, the location of centre of mass of the system of masses remains constant even when the individual masses move some distance relative to each other.

  $\begin{array}{l}{m}_1{d}_1=m_2{d}_2\\ \text{Where }{m}_1,m_2\text{ are the masses and }{d}_1,d_2\text{ are their movement relative to the centre of mass}\end{array}$

Calculation:

Using the equation

  $\begin{array}{l}{m}_1{d}_1=m_2{d}_2\\ (60)d_1=(80)(12)\\ d_1=16\text{m}\end{array}$

Distance between the two astronauts is given as

  $\begin{array}{l}d=d_1+d_2\\ d=16+12\\ d=28\text{m}\end{array}$

Conclusion:

Therefore, the distance between the two astronauts is 28 m.