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A projectile is fired at an angle theta...


A projectile is fired at an angle `theta` with the horizontal. Find the condition under which it lands perpendicular on an inclined plane inclination `alpha` as shown figure.

A

`sinalpha=cos(theta-alpha)`

B

`cosalpha=sin(theta-alpha)`

C

`tantheta=cot(theta-alpha)`

D

`cot(theta-alpha)=2tanalpha`

Text Solution

Verified by Experts

The correct Answer is:
D

Applying equation of motion perpendicular to the incline for `y=0`.
`0=Vsin(theta-a)t+(1)/(2)(-gcosalpha)t^2`
`t=0` & `(2Vsin(theta-alpha))/(gcosalpha)`
`Vsin(theta-alpha)`
At the moment of striking the plane, as velocity is perpendicular to the inclined plane hence component of velocity along incline must be zero.
`0=vcos(theta-alpha)+(-gsinalpha)`.
`(2Vsin(theta-alpha))/(gcosalpha)`
`vcos(theta-alpha)=tanalpha.2vsin(theta-alpha)`
`cot(theta-alpha)=2tanalpha`
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