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A ball falls freely form a height onto a...

A ball falls freely form a height onto and smooth inclined plane forming an angle a with the horizontal. Find the ratio of the distance between the points at which the jumping ball strikes the inclined plane. Assume the impacts to be elastic.

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On impact at point P. the velocity of the ball,`v = sqrt(2gh)`. Since the ball rebounds elastically, it gets deflected with the same velocity at an angle 8. From the geometry. `theta=a`The distance (PP) where it makes second impact is its range. The motion of the particle along the plane has speed v sin a and acceleration ng sind. The motion along the direction normal to the plane is with velocity v cos a and acceleration - cosa. Hence the time of flight T is given by y=0
. y = 0=v cos`aT-(1)/(2)gcosaT^(2)`or`T=(2v)/(g)`
Now l=vsina`T+(1)/(2)gsinaT^(2)`
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