Question

From a lift moving upward with a uniform acceleration $a$, a man throws a ball vertically upwards with a velocity $v$ relative to the lift. The ball comes back to the man after time $t$. Which relation is correct ?

• A. $a+g=3v/t$
• B. $a+g=v/t$
• C. $a+g=4v/t$
• D. $a+g=2v/t$

Answer 1

The correct option is D $a+g=2v/t$

Let us consider all the motion from lift frame. Then the acceleration, displacement and velocity everything will be considered from the lift frame itself.

As the ball comes again to the man, then displacement from the lift frame is zero. Again, the velocity with respect to the lift frame is $v$.

Similarly, the acceleration with respect to the lift frame is,

$g–(–a)=a+g\text{downwards}$

Now, using equation of motion,

$s=ut+\frac{1}{2}a{t}^2\Rightarrow 0=vt-\frac{1}{2}(a+g)t^2$

$\Rightarrow a+g=\frac{2v}{t}$

Hence, option $\left(a\right)$ is correct.

$$\begin{array}{c}\text{Why this question ?}\\ \text{For a projectile in an accelerating lift:-}\\ \text{Acceleration of projectile w.r.t lift =}\\ \text{Acceleration of projectile w.r.t ground}\\ \text{- Acceleration of lift w.r.t ground.}\end{array}$$