Question

A ball of mass $400gm$ is dropped from a height of $5m$ A boy on the ground hits the ball vertically upwards with a bat with an average force of $100N$ so that it attains a vertical height of $20m$. The time for which the ball remains in contact with the bat is$[g=10m/s^2]$

• A. $0.12s$
• B. $0.08s$
• C. $0.04s$
• D. $12s$

Answer 1

Answer: (A)

Velocity by which the ball hits the bat

$v_1=\sqrt{2g{h}_1}$

$=\sqrt{2\times 10\times 5}$ or ${\vec{v}}_1=+10m/s=10m/s$

Velocity of rebound

$v_2=\sqrt{2g{h}_2}$

$=\sqrt{2\times 10\times 20}=20m/s$ or ${\vec{v}}_2=-20m/s$

$F=m\frac{dv}{dt}=\frac{m\left({\vec{v}}_2-{\vec{v}}_1\right)}{dt}$

$=\frac{0.4\left(-20-10\right)}{dt}=100N$

by solving, $dt=0.12sec$