3. An exceptionally strong child finds himself coasting toward the right in cart

Question

3. An exceptionally strong child finds himself coasting toward the right in cart Cat constant velocity of 8.00 ft/s on a frictionless, horizontal surface (at point A). Child and car together weigh 96.0 lbs, and the child is carrying a ball, B, that weighs 32.0 lbs. As he sees the approaching edge of a steep frictionless slope, he hurls ball, B, to the left to try to make himself move even faster. The ball B leaves the child and car at a velocity of 58.0 ft/s with respect to the earth. His car then goes over the brink of the hill, its center of gravity dropping 25.0 ft to another horizontal, f surface, H, where the child and car collide with another stationary car, E, of weight 64.0 lbs. The coefficient of restitution is 0.500. (a) Find the initial speed of car C before collision at the bottom of the slope at H. (b) Find the final velocity of car E after collision 58.0 ft/s 25.0 ft

Explanation / Answer

Acc to conservation of momentum, initial momentum=final momentum

M+m×8=m×-50+M×v

(96+32)8=32×-50+96× v

V=27.33ft/s

1/2M(v2-u2)=Mgh substitute u= 27.3,h=25ft we will get

V=35.17ft/s

Mass of the car E is M'

Mu +M'u'=MV+M'V'

96×35.17=96×V+64V'(1)

V'-V/u-u'=0.5

V'-V=.5×35.17=17.6

V'=17.6+V (2)subsitut eq 2in 1 we get

V=14.06ft/s and V'= 31.66Ft/s

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