Question

A man of mass $50\text{kg}$ jumps on a car from a tower as shown in the figure.

Find the final velocity of the car if the weight of the car is $150\text{kg}$ and is initially moving with a velocity of $60\text{m/s}$.

• A. $45\text{m/s}$
• B. $150\text{m/s}$
• C. $90\text{m/s}$
• D. $30\text{m/s}$

Answer 1

The correct option is A $45\text{m/s}$

Given:
Mass of man $M_m=50\text{kg}$
Mass of car, $M_c=150\text{kg}$
Initial velocity of car, $v_i=60\text{m/s}$
Initial velocity of man in horizontal direction is $0\text{m/s}$
Let final velocity of (car+man) is $v_f$
As there are no external forces in horizontal direction, therefore applying conservation of linear momentum in horizontal direction.
$\Rightarrow M_c{v}_i=(M_c+M_m)v_f$
$\Rightarrow v_f=\frac{M_c{v}_i}{M_c+M_m}$
$=\frac{150\times 60}{200}=45\text{m/s}$