A roller-coaster is at the top of a 62-meter hill. The car and its passengers have a total mass of 1,088 kilograms. By the time the car reaches the bottom of the hill, its speed is 74 miles per hour (33 meters per second). How much kinetic energy does the car have at the bottom of the hill?
First, we need to calculate the potential energy at the top of the hill, which will be converted into kinetic energy at the bottom.
The potential energy at the top of the hill can be calculated using the formula:
PE = mgh
Where:
m = mass of the car and passengers = 1088 kg
g = acceleration due to gravity = 9.81 m/s^2
h = height of the hill = 62 meters
PE = 1088 * 9.81 * 62
PE = 670,654.56 Joules
At the bottom of the hill, this potential energy is completely converted into kinetic energy:
KE = 1/2 * mv^2
Where:
m = 1088 kg
v = 33 m/s
KE = 1/2 * 1088 * 33^2
KE = 597,648 Joules
Therefore, the car has 597,648 Joules of kinetic energy at the bottom of the hill.