Question

A roller-coaster car is at the top of a hill. The car and its passengers have a combined mass of 1,090 kilograms. If the hill is 65 meters tall how much potential energy does the car have? Acceleration due to gravity is 9.8 meters per second squared.



(1 point)
Responses

67,456.0 J
67,456.0 J

70,850.0 J
70,850.0 J

661,068.8 J
661,068.8 J

694,330.0 J

Answer 1

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:

\[
PE = m \cdot g \cdot h
\]

where:
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (in meters per second squared),
- \( h \) is the height (in meters).

Plugging in the given values:
- \( m = 1,090 \) kg,
- \( g = 9.8 \) m/s²,
- \( h = 65 \) m.

Now calculate the potential energy:

\[
PE = 1,090 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 65 \, \text{m}
\]

\[
PE = 1,090 \cdot 9.8 \cdot 65
\]

Calculating this step-by-step:

1. \( 9.8 \cdot 65 = 637 \)
2. \( 1,090 \cdot 637 = 694,330 \, \text{J} \)

Thus, the potential energy is:

\[
PE = 694,330.0 \, \text{J}
\]

The correct answer is:

**694,330.0 J**