Two particles A and B are projected with same speed so that the ratio of their maximum height reached is 3 : 1. If the speed of A is doubled without altering other parameters, the ratio of the horizontal ranges attained by A and B is

Options

A. `1:1`
B. `2:1`
C. `4:1`
D. `3:2`

Answer

C

Explanation

`H = (u^(2) sin^(2)theta)/(2g) rArr H_(1)/H_(2) = (sin^(2)theta_(1))/(sin^(2)theta_(2)) = 31`
`rArr (sin theta_(1))/(sin theta_(2)) = sqrt(3)/1`
By eq. (i) we conclude that our angle is also constant Then- `R prop u^(2)`
`R_(1)/R_(2) = ((2u)^(2)/u^(2)) rArr (4u^(2))/u^(2) = 4/1`
`R_(1) : R_(2) = 4:1`