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 = 10.3 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 ? = 0.183 kg/s. Initially, bucket and skateboard are moving at a speed of v0. How long will it take before the speed is reduced to 45.7%?

Explanation / Answer

As we know the basic Equation

Chance in Velocity = Initial velocity*ln(Initla mass/Final Mass)

Let the required time = t sec

Therefore

Final Mass = 10.3-0.183t

Thererfore

(100-45.7)/100 v = v * ln(10.3/(10.3-0.183t))

Therefore

0.543 = ln(10.3/(10.3-0.183t))

1.721 = (10.3/(10.3-0.183t))

Therefore

t = 23.6 sec

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