Question

From a building two balls A & B are thrown such that A is thrown upwards and B downwards (both vertically with same speed). If $V_A$ and $V_B$ are their respective velocities on reaching the ground then :

• A. $V_B<V_A$
• B. $V_A=V_B$
• C. $V_A<V_B$
• D. Their velocities depends on their masses

Answer 1

The correct option is B $V_A=V_B$

For A:
$s_A=v{t}_1-\frac{1}{2}g{t}_1^2$
$s_B=-v{t}_2-\frac{1}{2}g{t}_2^2$

We have, $s_A=s_B$

So, on solving we get:

$t_2-t_1=\frac{2v}{g}$ ...........(1)

Also,
$v_A=u_A-g{t}_1$
$v_B=u_B-g{t}_2$

Using $\left(1\right)$, we get:

$\frac{v_A}{v_B}=\frac{v-g{t}_1}{-v-g{t}_2}$$=\frac{v-g{t}_1}{-v-g(t_1+\frac{2v}{g})}=1$

$\Rightarrow v_A=v_B$