3. You are a prop designer for a Spider Man musical on Broadway; since it isa pl

Question

3. You are a prop designer for a Spider Man musical on Broadway; since it isa play, all stunts must be live-action. The script calls for Green Goblin to nudge Mary Jane off the top of a 15 m tall building set; Spider Man then dives straight downward from the same spot on the roof in an attempt to save her. After Mary Jane begins to fall, it takes Spider Man 0.25 s to begin his downward pursuit. You are designing web spinner props that allow him to generate downward thrust (force) and accelerate faster than with gravity alone in order to catch her. The actor playing the part weighs 150 pounds (68 kg). Estimate the minimum force that these web spinners must exert on the actor's wrists in order for him to catch Mary Jane before she lands (they will both be wearing safety harnesses, so you don't need to worry about what happens after he catches her - he just needs to catch her before she reaches the "ground" on the set).

Explanation / Answer

When Mary begins to fall she needs to cover a distance of 15 metres to reach ground.

As she falls with zero initial velocity,and with acceleration ,g. we have

S=ut +1/2 at²

Where sis distance=15m, .U=0 and a=g=9.8m/s²

We will find time which Mary will take to reach ground.

15=0.t +1/2(9.8)t²

t²=15*2/9.8

t²=3.06

t=1.75 second.

As spider Man starts his motion 0.25s later ,he has to catch Mary in 1.50 seconds of his motion,or he must cover the distance in 1.50 seconds.

Let extra thrust be F

We have

S=ut+1/2at²

a=force/mass

Here forces are due to gravity mg, and F

a=mg+F/m

a=g+F/m

Put values in above equation we have

15=0.t+1/2(9.8+F/m)(1.5)²

Solving this we get

30/2.25=(9.8+F/m)

13.33-9.8=F/m

3.533*m=F

F=3.533*68

F=240N

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