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Pankaj and sudhir are playing with two d...

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.

A

`2:1 `

B

`1:1`

C

`1 : cos theta `

D

`1: sec theta `

Text Solution

Verified by Experts

Let `u_(1)` and `u_(2)` be the initial velocities respectively. If `h_(1)` and `h_(2)` are the heights attained by them, then
`h1 = (u ^ ( 2) )/ ( 2g ) and h^(2) = ( u^(2)sin ^(2) theta )/(2g)`
The times of ascent of balls are equal , we have `= u//g = u_(2)sin theta //g`
`:. u_(1) = u_(2) sin theta `
From eq .`(A)(h^1)/(h_2)=(u_(1)^(2))/(u_(2)^(2)sin^2 theta`
From (B)&(C) , `(h_(1))/ h_(2) = (1)/(2)`
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