A helicopter is traveling at 40 m/s at a constant altitude of 100 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)40 m/s B)50 m/s C)60 m/s D)70 m/s

Question

Quizplus · Accepted Answer

The horizontal velocity of the helicopter does not affect the vertical acceleration of the wheel due to gravity. Therefore, the only force acting on the wheel is its weight, given by mg, where m is the mass of the wheel and g is the acceleration due to gravity. The initial vertical velocity of the wheel is zero. Using the equation of motion, h = ut + 1/2 gt^2, where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time, we can find the time it takes for the wheel to hit the ground.

h = ut + 1/2 gt^2 
100 = 0t + 1/2 (9.8) t^2 
t = sqrt(100/4.9)

t ≈ 6.43 seconds

Using the equation, v = gt, where v is the final velocity, g is the acceleration due to gravity, and t is the time, we can find the final velocity of the wheel.

v = gt 
v = 9.8 x 6.43 
v ≈ 63 m/s

Therefore, the wheel will hit the ground with a speed of approximately 63 m/s, which is closest to option C) 60 m/S.

A Helicopter Is Traveling at 40 M/s at a Constant