Agent 0007 James Bond (mass 75.0 kg), having survived the jump from one building

Question

Agent 0007 James Bond (mass 75.0 kg), having survived the jump from one building to another, now finds himself starting from rest and swinging down from a platform on a 7.00 m-long rope. At the bottom of the Archie speed is 8.40 m/s. What is the height of the platform? What is the tension in the rope when agent 0007 is at the bottom of the swing just before he catches his partner? At the bottom of the arc agent 0007 catches his partner (who is 60 kg) and was initially at rest and the two swing up together. Treating this a perfectly I elastic collision, what speed are they traveling just after they catch each other? What is the work done on James Bond by the tension in the rope as he is swinging down the platform ?

Explanation / Answer

by conservation of energy

initial energy = final energy

mgh = 0.5 * mv^2 + 0.5 * I * (v/r)^2

mgh = 0.5 * mv^2 + 0.5 * mr^2 * (v/r)^2

gh = 0.5 * v^2 + 0.5 * v^2

9.8 * h = 8.4^2

height of the platform h = 7.2 m

tension = mg + mv^2 / r

tension = 75 * 9.8 + 75 * 8.4^2 / 7

tension = 1491 N

by conservation of momentum

initial momentum = final momentum

75 * 8.4 = (75 + 60) * v

v = 4.67 m/s

final velocity = 4.67 m/s

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