Because of your knowledge of physics, you have been hired as a technical adviser

Question

Because of your knowledge of physics, you have been hired as a technical adviser on a new action movie. In one scene, the hero pursues the villain to the top of a very tall crane. The villain creates a diversion by dropping a bottle filled with deadly gas onto the unsuspecting crowd below. The script calls for the hero to quickly strap on a bungee cord with length L=100.00 ft and jump straight down to grab the bottle out of the air just as bungee cord begins to stretch. Your job is to determine the feasibility of the stunt by finding the initial speed vi with which the hero needs to jump downward to catch the bottle. You estimate that the hero can react to the villain's dropping the bottle by strapping on the bungee cord and jumping in to=2.00 s .

Explanation / Answer

here ,

L = 100 feet

the height dropped by the hero , h = 100 feet

acceeleration due to gravity , g = 32.17 feet/s^2

According to the problem the hero react in 2 seconds

time taken for the bottle to fall (with no V)i:

t = sqrt(2 * h/g)

t = sqrt(2 * 100/32.17)

t = 2.49s

So, if the hero reacts in the moment that the villan dropped the bottle and he takes 2 seconds to jump, he has only 0.49 seconds to fall

d= Vi*t + 0.5 (a*t^2)

100= Vi*0.49 + 0.5 (32.17*0.49^2)

Vi= 196.199 feet/s

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