Question

A man in a lift ascending with an upward acceleration throws a ball vertically upwards and catches it after $t_1$ second. Later when the lift is descending with the same acceleration, the man throws the ball up again with same velocity and catches it after $t_2$ second.
A) The acceleration of the elevator is $g\frac{(t_2-t_1)}{(t_1+t_2)}$
B) The velocity of projection of the ball relative to elevator is $\frac{t_2{t}_{1}g}{t_1+t_2}$.
We can conclude that:

• A. only $A$ is true
• B. only $B$ is true
• C. Both $A$ and $B$ is true
• D. Both $A$ and $B$ are false

Answer 1

The correct option is C Both $A$ and $B$ is true

We know that

$t_1=\frac{2u}{g+a}\&t_2=\frac{2u}{g-a}$

We get,

$2u=t_1(g+a)=t_2(g-a)a(t_1+t_2)=g(t_2-t_2)a=\frac{g(t_2-t_1)}{t_1+t_2}$

Now, the velocity of projection of the ball relative to elevator is u, We have,
$g+a=\frac{2u}{t_1}$
$g-a=\frac{2u}{t_2}$

adding both,
$2g=2u(\frac{1}{t_1}+\frac{1}{t_1})$

$\therefore u=\frac{t_1{t}_{2}g}{t_1+t_2}$