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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) propR^(2)`

B

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

C

`t_(1)t_(2) prop1/R`

D

`t_(1)t_(2) prop1/(R^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
For same range angle of projection should be `theta and (90^(@)- theta)`
So, time of flights `t_(1)=(2u sin theta)/g` and
`t_(2)=(2u sin(90^(@)-theta))/g=(2u cos theta)/g`
By multioplying `=t_(1)t_(2)=(4u^(2)sin theta cos theta)/(g^(2))`
`t_(1)t_(2)=(2)/(g) ((u^(2) sin 2 theta))/(g)=(2R)/(g)implies t_(1)t_(2) prop R`
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