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 fill with deadly gas onto the unsuspecting crowd below. The script calls for the hero to quickly strap on a 100 ft. bungee cord and jump straight down to grab the bottle out of the air just as the bungee cord begins to stretch. Your job is to determine the feasibility of the stunt by finding the initial speed 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 2.0 seconds. THE ANSWER IS NOT 187 OR 196.

Answer 1

consider the motion in down direction

v_i = initial velocity = 0 m/s

a = acceleration = 32.2 ft/s²

Y = vertical displacement = 100 ft

t = time of travel

using the equation

Y = v_i t + (0.5) a t²

100 = (0) t + (0.5) (32.2) t²

t = 2.492 sec

now , 2 sec are used in strapping the cord and jumping, so

t' = new time of travel = 2.492 - 2 = 0.492 sec

v_i = initial velocity = ?

a = acceleration = 32.2 ft/s²

Y = vertical displacement = 100 ft

Using the equation

Y = v_i t' + (0.5) a t'²

100 = v_i (0.492) + (0.5) (32.3) (0.492)²

v_i = 195.31 ft/s