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A projectile can have the same range R f...

A projectile can have the same range R for two angles of projection. If `t_(1)` and `t_(2)` be the times of flight in the two cases:-

A

`t_(1)t_(2) prop R^(2)`

B

`t_(1) t_(2) prop R`

C

`t_(1) t_(2) prop (1)/(R )`

D

`t_(1) t_(2) prop (1)/(R^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
The horizontal range is tahe same for the angles of 12. Use o = tat projection `theta and (90^(@)-theta)`
`t_(1)=(2u sin theta)/(g)`
`t_(2)=(2u sin (90^(@)-theta))/(g)=(2u cos theta)/(g)`
`t_(1)t_(2)=(2u sin theta)/(g)xx(2u cos theta)/(g)`
`(2)/(g)[(u^(2) sin 2 theta)/(g)]=(2)/(g)R`
where `R=(u^(2) sin theta)/(g)`
Hence, `t_(1)t_(2) prop R`
As g is constant
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