simply pulley/rope system, a crewman on an Arctic expedition is trying to lower

Question

simply pulley/rope system, a crewman on an Arctic expedition is trying to lower a 6.95-kg crate to the bottom of a steep ravine ofheight 27.5 meters. The 45.0-kg crewman is walking along holding the rope, being careful to lower the crate at a constant speed of 1.50 m/s. Unfortunately, when the crate reaches a point 15.3 meters above the ground, the crewman steps on a slick patch of ice and slips. 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

given,

height = 27.5 m

mass of crate = 6.95 kg

mass of crewman = 45 kg

initial speed = 1.5 m/s

after reaching 15.3 m he slips

v^2 + u^2 + 2as

v^2 = 1.5^2 + 2 * 9.8 * (27.5 - 15.3)

v = 15.536 m/s

crate will hit the ground with the speed of 15.536 m/s

vertical speed of crewman

v^2 = 2 * 9.8 * 27.5

v = 23.216 m/s

horizontal speed = 15.536 m/s

net speed = sqrt(15.536^2 + 23.216^2)

speed with which crewman will hit the bottom = 27.9347 m/s

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