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

ID: 2092390 • Letter: A

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 = 15.5 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 ? = 0.127 kg/s. Initially, bucket and skateboard are moving at a speed of v0. How long will it take before the speed is reduced to 28.5%?

Explanation / Answer

the velocity has to become 0.285 V0


F= Vdm/dt = V * 0.127

a= F/m = -V * 0.127 /15.5

a= dv/dt


V * 0.127 /15.5 =-dv/dt

dv/V = -122 dt/122

now we integrate it

ln v = t/122

ln (v/v0) =- t/122

t = - 122 ln(0.285) = 153 seconds