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Question

A smooth sphere of mass m is moving on a horizontal plane with velocity 3ˆi+ˆj. It collides with a vertical wall which is parallel to vectorˆj. If the coefficient of restitution is 0.5, the angle of velocity of the ball with repect to the normal to the wall after impact will be

A
30o
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B
tan1(13)
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C
cos1(213)
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D
sin1(213)
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Solution

The correct option is D sin1(213)
Coefficient of restitution
e = Relative velocity after collisionRelative velocity beore collision = ΔufinalΔuinitial = 0.5uinitial = 3 ˆi +ˆjΔuinitial = 3 (the wall is parallel to ˆj)Δufinal3 = 0.5 Δufinal = 32ufinal =32 ˆi +ˆj



sin θ = 1(32)2+12 = 213


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