A ball of mass m is thrown vertically upward. Another ball of mass 2m is thrown making an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is 1/x. The value of x i s_________.
Physics · Kinematics part-2 Projectile Motion · Motion in 2-D and ground to ground projectile
JEE Advanced 2022

Question

A ball of mass m is thrown vertically upward. Another ball of mass 2m is thrown making an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is 1/x. The value of x i s_________.

Physics · Kinematics part-2 Projectile Motion · Motion in 2-D and ground to ground projectile

JEE Advanced 2022

G1 Physics · Accepted Answer

Time of flight depends only on the initial vertical component: T = 2uᵧ/g. Since both balls stay in air for the same time, their vertical components are equal. Maximum height H = uᵧ²/(2g), so both attain equal heights. Thus H₁/H₂ = 1 = 1/x, giving x = 1.