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------------------------------------------------ A roller coaster with a potential energy of [tex]$235,200 \, \text{J}$[/tex] sits at the top of a 30 m high hill. What is the mass of the roller coaster?

(Formula: [tex]PE = mgh[/tex])

A. 800 kg
B. 7,840 kg
C. 8,000 kg
D. 78,400 kg

To find the mass of the roller coaster, we can use the formula for potential energy:

[tex]\[ PE = m \times g \times h \][/tex]

Where:
- [tex]$ PE $[/tex] is the potential energy in joules (235,200 J in this case)
- [tex]$ m $[/tex] is the mass in kilograms
- [tex]$ g $[/tex] is the acceleration due to gravity (approximately 9.8 m/s²)
- [tex]$ h $[/tex] is the height in meters (30 m in this case)

We need to solve for the mass [tex]$ m $[/tex]. Rearrange the formula to solve for [tex]$ m $[/tex]:

[tex]\[ m = \frac{PE}{g \times h} \][/tex]

Now, plug the values into the formula:

[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]

[tex]\[ m = \frac{235,200}{294} \][/tex]

[tex]\[ m = 800 \, \text{kg} \][/tex]

So, the mass of the roller coaster is 800 kg.