Question

In bungee jumping, a bungee jump is the amount the cord will stretch at the bottom of the tall. The stiffness of the cord is related to the amount of stretch by the 2WSL) equation K- s? 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 is the stretch in feet Use this equation to answer parts (a) and (b) (a) A 180-pound person plans to jump off a lodge attached to a cord of length 34 foot. If the stiffness of the cord is no less than 21 pounds per foot, how much will the cord stretch? A more than 34 feet B. less than 34 foet Cless than 35 feet Dexactly 34 feet DE between 34 and 35 feet (b) If safety requirements will not permit the jumper to get any closer than 3 feet to the ground, what is the minimum height required for the lodge in part (a)? The minimum safe height is feet above the ground

Answer 1

The bungee cord will stretch less than 34 feet and the minimum safe height for the lodge is exactly 34 feet.

Step-by-step explanation:

To find the stretch of the bungee cord, we can use the equation K = Ws, where W is the weight of the jumper, K is the cord's stiffness, and s is the stretch of the cord. In this case, W = 180 pounds and K is given to be no less than 21 pounds per foot. We can rearrange the equation to solve for s: s = K/W. Plugging in the values, s = 21 pounds per foot / 180 pounds = 0.1167 feet. Therefore, the cord will stretch approximately 0.1167 feet or about 0.14 feet (rounded to the nearest hundredth). This is less than 1 foot, so the answer is (B) less than 34 feet.

To find the minimum height required for the lodge, we can use the equation H = L + s, where H is the total height and L is the free length of the cord. Plugging in the values, H = 34 feet (given) + 0.1167 feet = 34.1167 feet. Therefore, the minimum safe height for the lodge is approximately 34.1167 feet or about 34 feet (rounded to the nearest hundredth). The answer is (D) exactly 34 feet.