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Question

A particle is projected at an angle α with the horizontal from the foot of a plane, whose inclination to the horizontal is β. What is the value of tan(αβ) if it strikes the plane at right angle?

A
cotβ2
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B
sinβ2
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C
tanβ2
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D
cosec β
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Solution

The correct option is A cotβ2

Let us analyze the values of initial velocity, final velocity and acceleration along X and Y axis
X - axisY- axisux=ucos(αβ)uy=usin(αβ)vx=0vy=?ax=gsinβay=gcosβ
If final velocity v is perpendicular to plane,
Time of flight T=2usin(αβ)gcosβ
Also, using first equation of motion,
vx=ux+at=ucos(αβ)gsinβ×T=0

ucos(αβ)=(gsinβ)2usin(αβ)gcosβcosβ=2tan(αβ)sinβtan(αβ)=cotβ2

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