To determine the gravitational potential energy ([tex]\( E_g \)[/tex]) of a roller coaster car at a certain height, we can use the formula:
[tex]\[ E_g = mgh \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height above the ground.
Given the values:
- [tex]\( m = 550 \)[/tex] kg (mass of the roller coaster car),
- [tex]\( g = 10 \, \frac{m}{s^2} \)[/tex] (acceleration due to gravity),
- [tex]\( h = 91 \)[/tex] m (height above the ground).
Let's plug these values into the formula:
[tex]\[ E_g = 550 \text{ kg} \times 10 \, \frac{m}{s^2} \times 91 \text{ m} \][/tex]
Now, multiply these numbers:
[tex]\[ E_g = 550 \times 10 \times 91 \][/tex]
[tex]\[ E_g = 550 \times 910 \][/tex]
[tex]\[ E_g = 500,500 \text{ J} \][/tex]
Hence, the gravitational potential energy ([tex]\( E_g \)[/tex]) of the roller coaster car is:
[tex]\[ E_g = 500,500 \text{ Joules} \][/tex]
