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A particle is projected with a certain v...

A particle is projected with a certain velocity at an angle `alpha` above the horizontal from the foot of an inclined plane of inclination `30^(@)`. If the particle strikes the plane normally then `alpha` is equal to

A

`30^@+tan^(-1)(sqrt(3)//2)`

B

`45^@`

C

`60^@`

D

`30^@+tan^(-1)(2-sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
A
Along `bot` r to incline plane.
`0=u sin (alpha-30^(@)) t-g( cos 30^(@))/(2) t^(2) rArr t=(2u sin (alpha-30^(@))/(g cos 30^(@))`
Particle strikes the plane normally velocity along the incline =0
`u cos (alpha-30^(@))=g sin 30^(@) t=0`
`rArr uc os (alpha -30^(@))=g sin 30^(@) 2u sin (alpha-30^(@))/(g cos 30^(@))`
`rArr tan (alpha-30^(@))=(cot 30^(@))/(2)=sqrt3/2 rArr alpha=30^(@)+tan^(-1) (sqrt3//2)`.
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