Choose the correct alternative `(s)`

Options

A. If the greatest height to which a man can throw a stone is `h`, then the greatest horizontal distance upto which he can throw the stone is `2h`.
B. The angl eof projection for a projectile motion whose range `r` is `n` times the maximum height is `tan^(-1)(4//n)`
C. The time of flight `T` and the horizontal range `R` of a parojectile are connected by the equaiton `gT^(2)=2R tan theta` where `theta` is the angle of projection.
D. A ball is thorwn vertically up. Another ball is thrown at an angle `theta` with the vertical. Both of them remian in air for the same period of time. Then the ratio of hieghts attained by the two balls `1:1`.

Answer

A, B, C, D

Explanation

(A) `(H)_(max) = (u^(2))/(2g) = h`
`R_(max) = (u^(2))/(g) rArr R_(max) = 2(u^(2))/(2g)`
`= 2h`
(B) `R = nh, (u^(2)sin 2 theta)/(g) = (n.u^(2)sin^(2) theta)/(2g)`
`rArr tan theta = (4)/(n)`
(C ) `2T^(2) = g((2usin theta)^(2))/(g) rArr 2T^(2) = (4u^(2)sin^(2) theta)/(g)`
`2T^(2) = (2xx u^(2)2 sin theta cos theta)/(g).(sin theta)/(cos theta)`
`rArr 2T^(2) = (2xx u^(2) sin^(2) theta)/(g) tan theta`
`2T^(2) = 2R tan theta`
(D) `T = (2u_(y))/(g), H = (u_(y)^(2))/(2g)`