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Q.

A small ball thrown with an initial velocity u directed at an angle θ = 37° above the horizontal collides inelastically (e = 1/4) with a vertical massive wall moving with a uniform horizontal velocity u/5 towards ball. After collision with the wall, the ball returns to the point from where it was thrown. Neglect friction between ball and wall. The time t from beginning of motion of the ball till the moment of its impact with the wall is (tan37° = 3/4)

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a

3u5g

b

18u25g

c

54u145g

d

54u25g

answer is C.

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Detailed Solution

Since the wall is frictionless , time of flight T =2u sin 370g=6u5gHorizontal component of velocity of the ball relative to the wall just after the impact =eurel=14(u5+u cos 370)=u4Therefore after the impact ,horizontal component of velocity of the ball relative to the ground = u5+u4=9u20So,( u cos 370+u5)t=9u20(6u5g-t) ⇒t=54 u145 g
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