Q 11-02-113JEE MainJEE Main 2021 (26 Aug, Shift 1)Medium
Two spherical balls having equal masses with radius of $5$ cm each are thrown upwards along the same vertical direction at an interval of $3$ s with the same initial velocity of $35$ m s$^{-1}$, then these balls collide at a height of ______ m. (take $g = 10$ m s$^{-2}$)
Numerical value type. Enter your answer.
Answer: 50
Let the first ball be thrown at $t = 0$. They meet when their heights are equal:
$$35t - 5t^2 = 35(t - 3) - 5(t - 3)^2 \Rightarrow 0 = -105 - 5(-6t + 9) \Rightarrow t = 5\ \text{s}$$
Height $= 35\times5 - 5\times25 = 50$ m (the $5$ cm radii make a negligible difference).
Solution by Sreeraj P, M.Sc Physics