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Answer :
We are given the potential energy of the roller coaster as
[tex]$$
PE = 235\,200 \text{ J}
$$[/tex]
and the height of the hill as
[tex]$$
h = 30 \text{ m}.
$$[/tex]
We know the formula for gravitational potential energy:
[tex]$$
PE = mgh,
$$[/tex]
where
[tex]\( m \)[/tex] is the mass in kilograms,
[tex]\( g \)[/tex] is the gravitational acceleration (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]), and
[tex]\( h \)[/tex] is the height in meters.
To find the mass, we rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]$$
m = \frac{PE}{gh}.
$$[/tex]
Substitute the given values into the equation:
[tex]$$
m = \frac{235\,200}{9.8 \times 30}.
$$[/tex]
First, calculate the denominator:
[tex]$$
9.8 \times 30 = 294.
$$[/tex]
Now, compute the mass:
[tex]$$
m = \frac{235\,200}{294} = 800 \text{ kg}.
$$[/tex]
Thus, the mass of the roller coaster is
[tex]$$
\boxed{800 \text{ kg}}.
$$[/tex]
[tex]$$
PE = 235\,200 \text{ J}
$$[/tex]
and the height of the hill as
[tex]$$
h = 30 \text{ m}.
$$[/tex]
We know the formula for gravitational potential energy:
[tex]$$
PE = mgh,
$$[/tex]
where
[tex]\( m \)[/tex] is the mass in kilograms,
[tex]\( g \)[/tex] is the gravitational acceleration (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]), and
[tex]\( h \)[/tex] is the height in meters.
To find the mass, we rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]$$
m = \frac{PE}{gh}.
$$[/tex]
Substitute the given values into the equation:
[tex]$$
m = \frac{235\,200}{9.8 \times 30}.
$$[/tex]
First, calculate the denominator:
[tex]$$
9.8 \times 30 = 294.
$$[/tex]
Now, compute the mass:
[tex]$$
m = \frac{235\,200}{294} = 800 \text{ kg}.
$$[/tex]
Thus, the mass of the roller coaster is
[tex]$$
\boxed{800 \text{ kg}}.
$$[/tex]
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