Question

A man and a plank of the same mass are moving with a velocity v along positive x-axis. At the same

time man jumps along negative x-axis with a velocity v with respect to ground, then the speed of the

plank is:​

Answer 1

Given:

A man and a plank of the same mass are moving with a velocity v along positive x-axis. At the same

time man jumps along negative x-axis with a velocity v with respect to ground.

To find:

Speed of plank ?

Calculation:

So, let me describe the events in this question in easy words:

• Both man and plank were together moving towards + x axis (rightwards) with velocity v.

• Now, the man jumped out with a velocity v towards -x axis (leftwards) from the plank.

• The question asks to find out the final velocity of the plank.

In this of questions, its best to use CONSERVATION OF LINEAR MOMENTUM, since no external force is involved.

$\sf \therefore \: P_{initial} = P_{final}$

$\sf \implies \:(m + m)v = m( - v) + m v_{plank}$

$\sf \implies \:2mv = - mv + m v_{plank}$

$\sf \implies \: m v_{plank} = 3mv$

$\sf \implies \: v_{plank} = 3v$

So, final velocity of plank is 3v towards +x axis (rightwards).