Question

A man of mass 60 kg jumps from a trolley of mass 20 kg standing on the smooth surface with absolute velocity 3 m/s. Find the velocity of a trolley and total energy produced by man:

• A. 90 m/s, 1.08 KJ
• B. 6 m/s, 1.20 KJ
• C. 7 m/s, 1.02 KJ
• D. 9 m/s, 1.08 KJ

Answer 1

The correct option is D 9 m/s, 1.08 KJ

In this their is no external force is acting so center of mass of the system will not move so

$M_1{v}_1+M_2{v}_2=0$ .... eq1

$M_1=60kg,M_2=20kg,v_1=3m{s}^{-1}$

$60\times 3+20\times v_2=0$

$\Rightarrow v_2=-9m{s}^{-1}$

negative sign indicate that trolley move opposite to the direction of the man velocity.

Energy produce by the man is used to give velocity to himself and the trolley

$E=\frac{1}{2}{M}_1{v}_1^2+\frac{1}{2}{M}_2{v}_2^2$

$\Rightarrow E=\frac{1}{2}\times 60\times 3^2+\frac{1}{2}\times 20\times 9^2=1.08KJ$

Hence the velocity of the trolley is $9m{s}^{-1}$ and energy produce by the man is $1.08KJ$