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A projectille can have the same range R ...

A projectille can have the same range` R` for two angles of projection. If ` t_(1)` and `t_(2)` be the time of flight in the two cases, then find the relation between ` t_(1), t_(2)` and `R` .

A

`R = sqrt(H_(1)H_(2))`

B

`R_(2) = H_(1)^(2) + H_(2)^(2)`

C

`R = H_(1) + H_(2)`

D

`R = 4sqrt(H_(1) H_(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`H_(1) = (u^(2) sin^(2) theta)/(2g)`
`H_(2) = (u^(2) sin^(2)(90^(@)-theta))/(2g) = (u^(2) cos^(2) theta)/(2g)`
and ` R = (u^(2) sin 2 theta)/g`
`H_(1) H_(2) = (u^(2) sin^(2) theta)/(2g) xx (u^(2) cos^(2) theta)/(2g)`
`rArr R = 4sqrt(H_(1) H_(2))`.
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