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
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