Question

in boot camp, a cadet must use a rope swing to cross an obstacle without falling into the water hazard below. unfortunately, they miss the platform on the other side and swing back to where they started. if it takes the cadet 5.5 seconds to swing from one side of the obstacle to the other and back, how long is the rope swing? use the formula: t = 2π√(l/9.8) a. 14.6 meters b. 4.7 meters c. 7.5 meters d. 2.9 meters

Explanation:

Step1: Substitute \(T = 5.5\) into the formula \(T=2\pi\sqrt{\frac{L}{9.8}}\)

We get \(5.5 = 2\pi\sqrt{\frac{L}{9.8}}\)

Step2: Solve for \(\sqrt{\frac{L}{9.8}}\)

Divide both sides by \(2\pi\): \(\sqrt{\frac{L}{9.8}}=\frac{5.5}{2\pi}\)
Since \(\pi\approx3.14\), then \(\frac{5.5}{2\times3.14}=\frac{5.5}{6.28}\approx0.876\)

Step3: Solve for \(L\)

Square both sides: \(\frac{L}{9.8}=(0.876)^2\approx0.767\)
Multiply both sides by \(9.8\): \(L = 0.767\times9.8\approx7.5\)

Answer:

C. 7.5 meters