You are riding on a roller coaster that starts from rest at a height of 25.0 m and moves down a frictionless track to a height of 3.00 m. how fast are you moving when you arrive at the 3.00-m height?

20.765 m/s

Explanation:

This problem can be solved by the conservation of energy principle, this means the initial energy must be equal to the final energy  :

(1)

Where each energy is the sum of kinetic energy and potential energy :

(2)

Where:

Being your mass and your initial velocity, since the roller coaster sterted from rest.

Being   the acceleration due gravity and   your initial height

Being your final velocity

Being your final height

Rewritting (2):

(3)

(4)

Isolating :

(5)

(6)

Finally:

This is your spedd when you arrive at 3 m height

the second one and the forth one are in the purple because they are opinions and the rest are in the yellow

explanation:

wavelength divides in half and speed stays the same.