If a roller coaster car had 40,000 J of gravitational potential energy when at rest on the top of a hill how much kinetic energy does it have when it is 3/4 of the way down the hill

K. E = 30,000 J

Explanation:

Given,

The potential energy of the roller coaster car, P. E = 40000 J

The kinetic energy at height h/4, K. E = ?

According to the law of conservation of energy, the total energy of the system is conserved.

At height 'h', the total energy is,

P. E = mgh

K. E = 0

At height 'h/4', the total energy is

P. E + K. E = mgh

P. E = mgh/4

K. E = 1/2 mv²

Therefore,

mgh/4 + 1/2 mv² = mgh

gh/4 + v²/2 = gh

Hence,

v² = 3gh/2

Substituting in the K. E equation

K. E = 1/2 mv²

= 1/2 m (3gh/2)

= 3/4 mgh

= 3/4 x 40000

= 30000 J

Hence, the K. E of the roller coaster car is, K. E = 30000 J