In one scene, the hero pursues the villain to the top of a very tall crane. The

Question

In one scene, the hero pursues the villain to the top of a very tall crane. The villain creates a diversion by dropping a battle filled with a deadly gas onto the unsuspecting crowd below. The script calls for the hero to quickly strap on a 100 ft bungee cord and jump straght down to grab the botle 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 villains dropping the bottle by strapping on the bungee cord and jumping in 2.o seconds.

A. What is the hero's required initial speed?

B. What is the algebraic expression for the hero's required initial speed in terms of the bungee cord (L), hero's reaction time (T), and the gravatational acceleration (g)?

Explanation / Answer

Hero's initial speed )v) should be such that he is able to catch the bottle at the length of the Bungee cable (L). I would solve in with variables. Substitute the value to get the answer.

So, L = vt + 0.5 gt^2. In the same time, the bottle has fallen by a distance through: L = 0.5 g(t+2)^2

So, vt + 0.5gt^2 = 0.5gt^2 + 2gt + 2g

=> t (v-2g) = 2g => t = 2g/(v-2g)

Substituting in the first expression: v = (L - 0.5 gt^2)/t where t = 2g/(v-2g)

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.