Question

Two stones are thrown from the top of a building with the same speed $u$, one in the upward direction and the other in the downward direction. When they reach the ground, they acquire certain velocities $v_1$ and $v_2$ respectively. What is the ratio of $v_1$ and $v_2$ ?

• A. 1:1
• B. 1:2
• C. 2:1
• D. 2:3

Answer 1

The correct option is A 1:1

Both stones reach the ground at the same point so their displacement is same.

Let displacement is $s$, Initial velocity of upward stone $u_1=u$,

Initial Velocity of downward stone $u_2=-u$,

Using $v^2=u^2+2as$,

$\Rightarrow v_1^2=u_1^2+2gs$ $\Rightarrow v_1^2=u^2+2gs$ ......1

$\Rightarrow v_2^2=u_2^2+2gs$ $\Rightarrow v_2^2=u^2+2gs$ ......2

Comparing equations 1 and 2, $\Rightarrow v_1^2=v_2^2$ $\Rightarrow v_1=v_2$,

$\Rightarrow v_1:v_2=1:1$