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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

Answer :

We are given the potential energy formula

[tex]$$
PE = m \cdot g \cdot h.
$$[/tex]

We need to solve for the mass [tex]$m$[/tex], so we rearrange the formula:

[tex]$$
m = \frac{PE}{g \cdot h}.
$$[/tex]

Substitute the given values into the formula:

[tex]$$
m = \frac{235200 \, \text{J}}{(9.8 \, \text{m/s}^2)(30 \, \text{m})}.
$$[/tex]

First, calculate the product in the denominator:

[tex]$$
9.8 \, \text{m/s}^2 \times 30 \, \text{m} = 294.
$$[/tex]

Now, divide the potential energy by this product:

[tex]$$
m = \frac{235200}{294} = 800.
$$[/tex]

Thus, the mass of the roller coaster is

[tex]$$
800 \, \text{kg}.
$$[/tex]

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