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A projectile can have same range R for t...

A projectile can have same range `R` for two angles of projection. It `t_1 and t_2` are the times of flight in the two cases, then what is the product of two times of flight ?

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
A projectile can have same range if angles of projection are complementary i.e. `theta` and `(90^(@) - theta)`. Thus, in both cases:
`t_(1) = (2u sin theta)/(g)`
`t_(2) 2usin (90^(@) - theta)/(g)`
`= (2u cos theta)/(g)`
From eq. (i) and (ii)
`t_(1)t_(2) = (4u sin theta cos theta)/(g^(2))`
`= (2u^(2)sin 2theta)/(g^(2))`
`:. t_(1)t_(2) = (2R)/(g) (therefore R = (u^(2)sin 2 theta)/(g))`
Hence, `t_(1)t_(2) prop R`
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