Question

Kaplit and mukesh are playing with two different balls of masses m and $2m$ respectively . If Kaplit throws his ball vertically up and Mukesh at an angle both of them stay in our view for the same period.The height attained by the two balls are in the ratio-

Answer 1

let's take the velocities ( of both balls ) as $v_0$ and $v_1$

Since time taken by both is equal, from the first law of motion, we see Vertical component of both velocities are equal

$v_{1}cos\theta =v_0$

$2gs=v^2-u^2$

$s_0=\frac{{v_0}^2}{2g}$

$s_1=\frac{{v_1}^2{cos}^2\theta }{2g}$

$\frac{s_1}{s_0}=\frac{\frac{{v_1}^2{cos}^2\theta }{2g}}{\frac{{v_0}^2}{2g}}=\frac{{v_1}^2{cos}^2\theta }{{v_0}^2}$