Question

A roller coaster car tops the highest point of the ride at 5 ft/s. The highest point of the ride is 100 feet above the ground. What is the velocity of the car at 10 feet above the ground. Use Conservation of Mechanical energy to solve this problem. Let ground be the reference level for the gravitational potential energy Round answer to 2 decimal places.Failure to follow directions will result in points lost. The car is traveling at _____________ m over s.

Answer 1

At the highest point, the car's velocity is 5 ft/s = 5 x 0.3048 m/s = 1.524 m/s v1 =  1.524 m/s
The highest point is 100 ft = 100 x 0.3048 m =30.48 m, h1 = 30.48 m
The total energy at the point,
TE = KE + PE = (1/2) m v12 + m g h1
We need to find the velocity of the car at 10 ft, h2 = 10 ft = 10 x 0.3048 = 3.048 m
The total energy at 10 ft
TE = KE + PE = (1/2) m v22 + m g h2
Using the conservation of mechanical energy,
(1/2) m v12 + m g h1  = (1/2) m v22 + m g h2  
(1/2) x (1.524 m/s)2 + 9.8 x 30.48 m = (1/2) x v22 + 9.8 x 3.048 m
v22 = -268.994888 x 2
v2 = 23.19 m/s