Question

A very broad elevator is going up vertically with a constant acceleration of $2m/s^2$. At the instant when its velocity is $4m/s$ a ball is projected from the floor of the lift with a speed of $4m/s$, relative to the floor at an elevation of ${30}^o$. The time taken by the ball to return the floor is
($g=10m/s^2$)

• A. $\frac{1}{2}s$
• B. $\frac{1}{3}s$
• C. $\frac{1}{4}s$
• D. $1s$

Answer 1

The correct option is B $\frac{1}{3}s$

Component of velocity of ball relative to lift are

$u_x=4\cos {30}^{\circ }=2\sqrt{3}m/s$

$u_y=4\sin {30}^{\circ }=2m/s$

and acceleration of ball relative to lift is $a=10+2=12m/s^2$ in negative y direction acting downwards.

Therefore Time of flight $T=\frac{2u_y}{a}$

$=\frac{2\times 2}{12}$

$=\frac{1}{3}s$