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Question

A ball is projected with initial velocity u at an angle θ to the horizontal. Then horizontal displacement covered by ball as it collides third time to the ground be, if coefficient of restitution is e, ______
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A
eu2sin2θg
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B
(1+e)u2sin2θg
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C
(1+e+e2)u2sin2θg
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D
(1e)u2sin2θg
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Solution

The correct option is C (1+e+e2)u2sin2θg
Range of the projectile with velocity u is given by R=u2sin2θg

so before first collision R1=u2sin2θg

now vertical velocity changes to euy as it is given that coefficient of restitution is e.

so before second collision R2=eu2sin2θg

similary before 3rd collision R3=e2u2sin2θg

Total displacement R=R1+R2+R3

R=u2sin2θg+eu2sin2θg+e2u2sin2θg

R=(1+e+e2)u2sin2θg

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