Two particles A and B are projected with same speed so that the ratio of their maximum heights reached is `3:1` . If the speed of A is doubled without altering other paramenters , 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)or(H_(1))/(H_(2))=(u^(2)sin^(2)theta_(1))/(u^(2)sin^(2)theta_(2))`
`or(3)/(1)=(sin^(2)theta_(1))/(sin^(2)theta_(2))or(sintheta_(1))/(sintheta_(2))=(sqrt(3))/(1)`
Logically , we can conclude that
`theta_(1)=60^(@),theta_(2)=30^(@)`
Again `R=(u^(2)sin2theta)/(g)`
or `(R_(1))/(R_(2))=(4u^(2)sin2theta_(1))/(u^(2)sin2theta_(2))`
or `(R_(1))/(R_(2))=(4sin2(60^(@)))/(sin2(30^(@)))=(4sin120^(@))/(sin60^(@))`
or `(R_(1))/(R_(2))=(4xx(sqrt(3))/(2))/((sqrt(3))/(2))=4`