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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_1t_2propR^2`

B

`t_1t_2propR`

C

`t_1t_2prop(1)/(R )`

D

`t_1t_2prop(1)/(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=(2usintheta)/(g)` and
`t_2=(2usin(90-theta))/(g)=(2ucostheta)/(g)`
By multiplying`=t_1t_2=(4u^2sinthetacostheta)/(g^2)`
`t_1t_2=(2)/(g)((u^2sin2theta))/(g)=(2R)/(g)impliest_1t_2propR`
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