Question

In bungee jumping, a bungee jump is the amount the cord will stretch at the bottom of the fall. The stiffness of the cord is related to the amount of stretch by the equation K= (2W(S+L))/S² , where W is the weight of the jumper in pounds, K is the cord's stiffness in pounds per foot, L is the free length of the cord in feet, and S is the stretch in feet.. Use this equation to answer parts (a) and (b). (a) A 110-pound person plans to jump off a ledge attached to a cord of length 51 feet. If the stiffness of the cord is no less than 22 pounds per foot, how much will the cord stretch?

A. more than 28 feet
B. exactly 28 feet
C. less than 28 feet
D. less than 29 feet
E. between 28 and 29 feet

Answer 1

Using the given stiffness equation and the values provided, the stretch of the bungee cord for a 110-pound person with a cord length of 51 feet and a stiffness of at least 22 pounds per foot is calculated to be less than 28 feet.

Step-by-step explanation:

We are given the formula for the stiffness of a bungee cord K = (2W(S+L))/S², where W is the weight of the jumper, K is the stiffness of the cord, L is the free length of the cord, and S is the stretch of the cord. We need to solve for S when a 110-pound person uses a 51-foot cord and the stiffness K is no less than 22 pounds per foot.

Let's insert the known values into the formula and solve for S.

22 = (2 × 110(S + 51))/S²

Simplifying and solving the quadratic equation, we find that the cord will stretch less than 28 feet, which corresponds to option C.