Calculate the Height of the Roller Coaster

14 Sep 2023

Question:

A roller coaster car has a mass of 1000 kg and gains 450,000 J of potential energy as it climbs a hill. How high is the hill?

The height of the hill can be calculated using the formula for potential energy. We can rearrange the formula to solve for height:

To calculate the height of the hill, we can use the formula for potential energy:

PE = m * g * h

Where:

PE = Potential Energy gained (450,000 J)

m = Mass of the roller coaster car (1000 kg)

g = Acceleration due to gravity (9.81 m/s^2)

h = Height of the hill

By rearranging the formula:

h = PE / (m * g)

Substitute the given values:

h = 450,000 J / (1000 kg * 9.81 m/s^2)

Calculating the height:

h = 450,000 J / 9810 m

h ≈ 45.88 meters

Therefore, the height of the hill that the roller coaster car climbs is approximately 45.88 meters.