A cart of mass M moves at a speed 17 m/s on a frictionless surface. At regular intervals of length 8m, blocks of mass m=M/2 drops vertically into the cart. How much time is taken to cover a distance of 36m ?
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Since no external force acts in horizontal direction (even when mass falls on the cart vertically),linear momentum will be conserved in the horizontal direction.
So, Initial monetum = 17M= Final momentum
Time taken to travel 8m = 8/17
After 8m, according to momentum conservation
17M = v*3M/2
Velocity = 34/3
Time taken to travel from 8m to 16m = 8*3/34 = 12/17
Similarly time taken to travel from 16m to 24m = 16/17
Time taken to travel from 24m to 32m = 20/17
Time taken to travel from 32m to 36m = 24/2*17 = 12/17
Total time taken = 8/17 + 12/17 + 16/17 + 20/17 + 12/17 = 4sec
Explanation:
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