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On an inclined plane two particles A and...

On an inclined plane two particles `A and B` are projected with same speed at the same angle with the horizontal, particle `A` down and particle `B` up the plane. If the ratio of time of flight of `A and B` is `cot theta`, where `theta` is the angle at which `B` is projected measured from inclined plane, find the angle at which particles are projected.

A

`90^@`

B

`60^@`

C

`30^@`

D

`45^@`

Text Solution

Verified by Experts

The correct Answer is:
D

`t_A=(2sin(alpha+beta))/(gcosbeta)` and `t_b=(2usin(alpha-beta))/(gcosbeta)`
`(t_A)/(t_B)=(sin(alpha+beta))/(sin(alpha+beta))=(costheta)/(sintheta)=(sin(90-theta))/(sintheta)`
`alpha+beta=90-thetaimpliesalpha=45^@`
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