Question

Rajat drops a ball of mass 100 g from building of height 20 m. After reaching to the ground, the ball bounces back with a velocity of $15m{s}^{-1}$. Determine its impulse. Take, $g=10m{s}^{-2}$.

• A. 3.5 Ns
• B. 0.5 Ns
• C. 1.5 Ns
• D. 2 Ns

Answer 1

The correct option is A 3.5 Ns

Let the upward direction be positive,
Given:
$m=100g=0.1kg$
$u=0m/s$
$a=-10m/s^2$
$s=-20m$
Velocity after bouncing, $v_f=+15m/s$

Velocity of the ball just before touching the ground can be found using the equation of motion.
$v^2=u^2+2as$
$v^2=0+2\times (-10)\times (-20)$
$v^2=400$
$v=\pm 20m/s$
$v=-20m/s$ (negative sign indicating downward direction)

Using definition of impulse,
$J=m\times (v_f-v)$
$J=0.1\times (15-(-20\left)\right)$
$J=3.5Ns$