# Question on Law conservation of Mechanical Energy

## Homework Statement

Assuming no friction or air resistance, calculate the height at C if at point A, the roller coaster had a speed of 20 m/s, and height of 0.45 km. The height at point B is 0 m. The speed at C is 15.6m/s.

So basically the roller coaster starts from A which is 0.45 Km high and moves forward (down) with a speed of 20m/s and the roller coaster dips down to point B where the height is 0 m. Then the roller coaster goes up to point C.

## Homework Equations

Eti = Etf (Initial mechanical energy = final mechanical energy)
Ek = mv^2/2
Eg= mgh
g= 9.80 m/s^2

## The Attempt at a Solution

I used the the law of mechanical energy equation and had to find the velocity of point B to move on to find the height of point c.
So using the given information and the equations, I found that the velocity at point B is 96 m/s (rounded to significant digits)and using the velocity of Point B and the other information given I was able to determine that the height is 0.457 km a point C.

But... the height for point c seems wrong according the diagram.
I could be wrong but I think point c should be less than the height of point A, according to the diagram.

Doc Al
Mentor
But... the height for point c seems wrong according the diagram.
I could be wrong but I think point c should be less than the height of point A, according to the diagram.
I haven't checked your calculations, but why would you think that point C should be lower than point A? I assume point C is meant to be the highest point reached by the coaster?

Conservation of energy

1/2mv^2 + mgh = 1/2mv^2 + mgh

you can drop the mass out since the mass is constant. thus,

1/2v1^2 + gh1 = 1/2v2^2 +gh2

Use a and b to find the speed at b, and then b and c to find the height at c

C should be higher, since the velocity at C is less than the velocity at A you can infer that the car has passed it's initial point. Since it had an initial velocity of 20 m/s you would expect it to have a final velocity of 20 m/s when it reached the dame height on the other side. however, the velocity is lower stating that it has traveled passed the point of equal height and slowed down more.