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For a given velocity, a projectile has t...

For a given velocity, a projectile has the same range `R` for two angles of rpojection if `t_(1)` and `t_(2)` are the times of flight in the two cases then

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
`t_(1) ( 2 u sin theta)/( g)`
`t_(2) = ( 2 u sin (90 - theta))/( g) = (2 u cos theta)/(g)`
`t_(1) . t_(2) = ( 4 u^(2) sin theta cos theta)/( g) = (2 u ^(2) sin 2 theta)/( g) = (2 R)/( g)`
`rArr R prop t_(1) t_(2)`
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