Information: When traveling at top speed, a roller coaster train with a mass of 12,000 kg has a velocity of 30 m/s. The kinetic energy of the train at top speed is 5,400,000 J. Math Proof:

KE = 1/2mv2

KE = 1/2(12,000kg)(30m/s)2

KE = 5,400,000J

5,400,000J = 1/2(12,000kg)(30m/s)2

More information: We can assume the KE and PE have an inverse relationship in this system. (Relationship in math and science is not love/Valentines. It is cause and effect; one thing affects another and vice-a-versa. Inverse means when two variables do the opposite. (E. g. When one goes up, the other goes down. When the other goes up, then the first goes down.)

Therefore PE = 5,400,000J, (same as the KE), but at an opposite point on the roller coaster track

Bonus challenge:

Using this formula and the math figures from above, can you calculate how tall the tallest hill was for this roller coaster ride? Please state your answer in meters.

PE = mgh

h=PE/(mg)

h=PE/(12,000kg x 9.8m/s2 )

h=