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(α−β) 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
cosecβ
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Solution
The correct option is Acotβ2
Let us analyze the values of initial velocity, final velocity and acceleration along X and Y axis X - axisY- axisux=ucos(α−β)uy=usin(α−β)vx=0vy=?ax=−gsinβay=−gcosβ
If final velocity v is perpendicular to plane,
Time of flight T=2usin(α−β)gcosβ
Also, using first equation of motion, vx=ux+at=ucos(α−β)−gsinβ×T=0