Using a simply pulley/rope system, a crewman on an Arctic expedition is trying t

Question

Using a simply pulley/rope system, a crewman on an Arctic expedition is trying to lower a 6.17 kg crate to the bottom of a steep ravine of height 23.0 meters. The 60.9 kg crewman is being careful to lower the crate at a constant speed of 1.50 m/s. Unfortunately, when the crate reaches a point 12.8 meters above the ground, the crewman slips and the crate immediately accelerates toward the ground, dragging the hapless crewman across the ice and toward the edge of the cliff. If we assume the ice is perfectly slick (that is, no friction between the crewman and the ice once he slips and falls down), at what speed will the crate hit the ground? Assume also that the rope is long enough to allow the crate to hit the ground before the crewman slides over the side of the cliff. At what speed will the crewman hit the bottom of the ravine? (Assume no air friction.)

Explanation / Answer

from the FBD we get the eq, T=ma, m= mass of the person, T-m2*g=m2*a, here m2 = mass of the block , T= tension in the rope, from the eqs we get a= 0.8144m/sec^2, now use v^2=u^2+2*a*s to get velocity of the block , v=4.93m/sec use the same eq to get the velocity of man before it hits the ground , Vm^2 = 0+2*9.8*23.9=> Vm=21.64m/sec

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