A bucket is mounted on a skateboard, which rolls across a horizontal road with n

Question

A bucket is mounted on a skateboard, which rolls across a horizontal road with no friction. Rain is falling vertically into the bucket. The bucket is filled with water, and the total mass of the skateboard, bucket, and water is M = 18.7 kg. The rain enters the top of the bucket and simultaneously leaks out of a hole at the bottom of the bucket at equal rates of ? = 0.161 kg/s. Initially, bucket and skateboard are moving at a speed of v0. How long will it take before the speed is reduced to 37.7%?

Explanation / Answer

net momentum will be conserved
let the time taken be t
in t time let M mass of water enters and leaves the bucket

now applying momentum cons.

18.7*v0 = 0.377v0 * 18.7 + M * 0.337*v0

from here M= 30.9 kg

time taken to enter and exit 30.9 kg of mass is = 30.9/0.161 = 191.94 sec = 3 min 12 sec

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