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Question

Two inclined planes intersect in a horizontal plane. their inclinations to the horizontal being α and β. If a particle is projected with velocity u at right angle to the former from a point on it, find the time after which the velocity vector will become perpendicular to the other inclined plane.

A
t=usin(α+β)gsinβ
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B
t=ucos(α+β)gcosβ
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C
t=ucos(α+β)gsinβ
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D
t=usin(α+β)gcosβ
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Solution

The correct option is B t=ucos(α+β)gcosβ
vcosβ=usinα
vsinβ=ucosαgt
usinαcosβsinβ=ucosαgt
usinαsinβ+ucosαcosβcosβ=gt
t=ucos(α+β)gcosβ
Hence,
option (B) is correct answer.

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