A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m. It coasts down a slope, and then climbs a hill. The top of the hill is at an elevation of 16 m. What is the speed of the car at the top of the hill? Neglect any frictional effects.
A) 14 m/s
B) 18 m/s
C) 10 m/s
D) 9.0 m/s
E) 6.0 m/s

Question

Quizplus · Accepted Answer

To solve this problem, we can use conservation of energy. At the top of the roller coaster, all of the energy is in the form of potential energy:

mgh = (1/2)mv^2

where m is the mass of the car, g is the acceleration due to gravity, h is the height above ground, and v is the speed of the car.

We can solve for v by plugging in values:

mgh = (1/2)mv^2 
mg(h - 16) = (1/2)mv^2  (using the height of the hill as the reference level)
2gh - 32g = v^2 
v = sqrt(2gh - 32g) = sqrt(2*9.81*10) = 14 m/s

So the answer is A) 14 m/s.

A Car on a Roller Coaster Starts at Zero Speed