Question

A man of mass 60kg and a boy of mass 30kg are standing together on a frictionless ice surface. If they push each other apart, man moves away with a speed of \[0.4m/s\] relative to ice. After 5sec they will be away from each other at a distance of.
$\begin{align}
  & \text{A}\text{. 9}\text{.0m} \\
 & \text{B}\text{. 3}\text{.0m} \\
 & \text{C}\text{. 6}\text{.0m} \\
 & \text{D}\text{. 30m} \\
\end{align}$

Answer 1

Hint: Use conservation of momentum which is defined as when two bodies act upon one another, their total momentum remains constant, provided no external forces are acting. From this law, calculate the velocity of a boy. Use relative velocity concept. Relative velocity is defined as, vector difference between the velocities of two bodies, the velocity of a body with respect to another regarded as being rest. Manipulate speed formula to calculate distance, where they will be away from each other.

Complete step by step solution:
In the question, a man and a boy standing together having masses $60kg$ and $30kg$ respectively. But these two people are moving in opposite directions, since they are pushing each other against each other.
Let, \[v\] be the speed of a boy and Speed of a man is \[0.4m/s\].
Given that after \[5sec\] they will reach at some distance.
So, according to law of conservation of momentum, we can say,
Momentum of man must be equal to the momentum of boy.
i.e. \[\text{momentum of man=momentum of boy}\]
We know that momentum is a product of mass and velocity.
Therefore,
\[\text{mass of man}\times \text{velocity of man = mass of boy}\times \text{velocity of boy}\]
\[60\times 0.4=30\times v\]
\[v=\dfrac{24}{30}=0.8m/s\]
Therefore relative velocity must be equal to sum of velocity of man and sum of velocity of boy.
\[\therefore \text{Relative velocity= 0}\text{.4+0}\text{.8=1}\text{.2m/s}\]
This is the distance where after \[5sec\] they reached
Now apply the formula of speed which is defined as distance per unit time.
\[v=\dfrac{\text{distance}}{t}\]
So,
\[\begin{align}
  & 1.2=\dfrac{\text{distance}}{0.5} \\
 & \text{distance=1}\text{.2}\times \text{0}\text{.5=6}\text{.0m} \\
\end{align}\]
After 5sec they will be away from each other at a distance of \[\text{6}\text{.0m}\]

Note: If both bodies have equal momentum then that means larger mass must have small velocity and smaller mass must have larger velocity. Since they have the same momentum, a lighter body will possess more kinetic energy. So as you can see in the solution, the speed of a boy is greater hence kinetic energy possessed by boy body will be more than man. Relative velocity is defined as, vector difference between the velocities of two bodies, the velocity of a body with respect to another regarded as being rest.