Question

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=

Answer 1

KE = PE
Work done = PE = KE
Wd = force * distance
Force = m.a
Distance = s
But a = v -u/t
v = final velocity
u = initial velocity
t = time
s = (t)(u + v)/2
KE = body starts from rest
Wd = m * (v-u/t) * (t)(u+v)/2
Wd = m * (v-0/t) * (t)(0+v)/2
Wd = m * (v-0) * (0+v)/2
Wd = m * (0 + v^2 - 0 + 0)/2
Wd = m * v^2 /2
Wd = 1/2 mv^2
Therefore if h=PE/(12000kg * 9.8m/s^2)
And PE=KE
h=5400000J/117600kgms^2
h=45918367.3m2/s4