Question 19 of 25 Correct Correct Map A sapling. earning Using a simply pulley/r

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Question 19 of 25 Correct Correct Map A sapling. earning Using a simply pulley/rope system, a crewman on 45.0 kg an Arctic expedition is trying to lower a crate to the bottom of a steep ravine of height crewman is walking frictionless 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 6.43 kg 14.1 meters above the ground, the crewman steps on a slick patch of ice and slips. The crate 25.4 m immediately accelerates toward the ground, dragging the hapless crewman across the ice and 14.1 m 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 figure not to scale enough to allow the crate to hit the ground before the crewman slides over the side of the cliff. Number At what speed will the crewman hit the bottom of the ravine? (Assume no air friction.) Number A Previous Check Answer Next Exit 8 Hint

Explanation / Answer

for the crate

m*g - T = m*a

for the crew man

T = M*a

m*g - M*a = m*a

a = mg/(m+M)

a = (6.43*9.8)/(6.43+45)

a = 1.22 m/s^2

v^2 - u^2 = 2*a*s

v^2 - 1.5^2 = 2*1.22*14.1

vy = 6.05 m/s

+++++++++

from v = u + a*t

6.05 = 1.5 + 1.22*t

t = 3.73 s

vx = 6.05 m/s

vy = sqrt(2*9.8*25.4)

vy = 22.3 m/s

speed = v = sqrt(vx^2+vy^2)

v = 23.11 m/s <<---answer

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