A helicopter is traveling at 50.0 m/s at a constant altitude of 150 m over a level field.If a wheel falls off the helicopter,with what speed will it hit the ground? (g = 9.8 m/s² and air resistance negligible) A)63 m/s B)55 m/s C)74 m/s D)54 m/s

Question

Quizplus · Accepted Answer

We can use the principle of conservation of energy to solve the problem. Initially, the helicopter has only kinetic energy (KE), and no potential energy (PE). When the wheel falls off, it loses contact with the helicopter and begins to fall under the force of gravity, gaining potential energy (PE) and losing KE. The total energy (KE + PE) of the system remains constant, so we can equate the initial KE of the wheel to its final PE when it hits the ground.

Initial KE = 1/2mv^2 = 1/2 * m * (50 m/s)^2 = 1250m
Final PE = mgh = m*g*h = m * 9.8 m/s^2 * 150 m = 1470m

Equating them, we get: 
1250m = 1470m
v = sqrt(2gh) = sqrt (2*9.8 m/s^2 * 150 m) = 54.4 m/s

Therefore, the speed with which the wheel hits the ground is approximately 54.4 m/s, which is closest to option C (74 m/s).

A Helicopter Is Traveling at 50