A roller coaster car is at the top of a hill. The car and it's passengers have a combined mass of 1,088 kilograms. If the hill is 62 meters tall, how much potential energy does the car have?

1 answer

To calculate the potential energy (PE) of the roller coaster car at the top of the hill, we can use the formula for gravitational potential energy:

\[ PE = mgh \]

where:

  • \( m \) is the mass (in kilograms),
  • \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
  • \( h \) is the height (in meters).

Given:

  • \( m = 1088 , \text{kg} \)
  • \( h = 62 , \text{m} \)
  • \( g = 9.81 , \text{m/s}^2 \)

We can now plug in the values:

\[ PE = 1088 , \text{kg} \times 9.81 , \text{m/s}^2 \times 62 , \text{m} \]

Calculating step-by-step:

  1. Calculate \( 9.81 \times 62 \): \[ 9.81 \times 62 = 609.42 , \text{m}^2/\text{s}^2 \]

  2. Now multiply by the mass: \[ PE = 1088 , \text{kg} \times 609.42 , \text{m}^2/\text{s}^2 = 663,125.76 , \text{J} \]

So, the potential energy of the roller coaster car at the top of the hill is approximately:

\[ PE \approx 663,126 , \text{J} \quad \text{(rounded to the nearest joule)} \]