What is the speed of the rollercoaster at point A?

Question

From ground level, a roller coaster (mass=250kg) ascends a ramp at a constant speed of 3 m/s for 22 seconds whereby it reaches the top of the ramp. It pauses for a moment at the top, and then rapidly descends. What is the speed of the rollercoaster at point A?

Answer 1

How high is point A, and what is the height from which the roller coaster is falling?  There is no diagram.  I can give you the approach, but not the final answer, without additional information.

 

H = height from which it falls, following the track, driven only by gravity

h = height at point A

 

If it starts from rest at a height of H, then it has only potential energy U.

 

U = mgH

 

That must equal the sum of kinetic and potential energy at point A.

 

mgH = (1/2)mv² + mgh

 

gH = v²/2 + gh

 

v = √[2g(H - h)]

 

As you can see, we need the 2 heights H and h.