# Roller Coaster Physics- Determining the highest point's height

1. Homework Statement [/b
]Here’s what you know: Mass is 750 Kg, Velocity is 20 m/s, Gravity remains at 10 m/s2 and Point B’s height is 15 m. Assume that Point A is the highest point and assume there is no friction for this problem.

Complete in the order that makes the best sense to you:
Calculate the total energy at Point A and Point B. Determine Point A’s height.

E= mgh + ½ mv2

## The Attempt at a Solution

Energy at Point B: (+ 4 pts)
E= mgh + ½ mv2
E= (750) (10) (15) + 0
E= 112500 J

I found the Ep for Point B. When I tried to work "backwards" by trying to find Point A's height by using Point B's Ep and height, I came up with a negative energy. I think there should be a way to use this known data to determine point A's height and Ep, but I can not figure it out.

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cepheid
Staff Emeritus
Gold Member
Welcome to PF angelbonnet,

It's not clear what's going on in the problem. Does the roller coaster start at point A or at point B? At what point does it have the velocity of 20 m/s?

If you can clarify these points, we should be able to help.

Thank you, The roller coaster starts at point A and the velocity is for point B.

cepheid
Staff Emeritus
Gold Member
Thank you, The roller coaster starts at point A and the velocity is for point B.
Okay, then your expression for the energy at point B is wrong, because you have not included the kinetic energy that the roller coaster has at point B due to its motion at 20 m/s.

Total energy is conserved, so the potential energy that the coaster loses in falling from point A to point B must be equal to the kinetic energy that it gains as a result.

You can use this fact to figure out what distance it must have fallen i.e. how much higher point A is than point B.

Thank you for the insights. I'll attempt it with these in mind.