Calculate the Height of the Roller Coaster
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?Answer:
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.