Pankaj and sudhir are playing with two different balls of masses `m and 2 m`, respectively. If Pankaj throws his ball vertically up and Sudhir at an angle `theta`, both the balls stay on our view for the same period. Find the ratio of the heights attained by the two balls.

Explanation

Time of flight for the ball thrown by pankaj, `T_1 = (2 u_1)/(g)`
Time of flight for the ball thrown by Sudhir,
`T_2 = (2 u_2 sin (90^@ - theta))/(g)`
`(2 u_2 cos theta)/(g)`
According to `T_1 = T_2 rArr (2 u_1)/(g) = (2 u_2 cos theta)/(g)`
`rArr u_1 = u_2 cos theta`
Height of the ball thrown by Pankaj, `H_1 = (u_1^2)/(2 g)`
Height of the ball thrown by Sudhir,
`H_(2) = (u_(2)^(2)sin^(2)(90^(@) - theta))/(2g) = (u_(2)^(2)cos^(2)theta)/(2g)`
`(H_(1))/(H_(2)) = (u_1^2//2 g)/(u_2^2 cos^2 theta// 2 g) = 1` `[as u_1 = u_2 cos theta]`.
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