Certainly! Let's solve this problem step by step using the given formula for potential energy:
The formula for potential energy (PE) is:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- \( PE \) is the potential energy,
- \( m \) is the mass,
- \( g \) is the gravitational acceleration, which is \( 9.8 \, \text{m/s}^2 \),
- \( h \) is the height.
Given the values:
[tex]\[ PE = 235,200 \, \text{J} \][/tex]
[tex]\[ h = 30 \, \text{m} \][/tex]
[tex]\[ g = 9.8 \, \text{m/s}^2 \][/tex]
We need to find the mass \( m \). To do this, we rearrange the formula to solve for \( m \):
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Now, substitute the known values into the equation:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \cdot 30 \, \text{m}} \][/tex]
Calculate the denominator first:
[tex]\[ 9.8 \, \text{m/s}^2 \cdot 30 \, \text{m} = 294 \, \text{m}^2/\text{s}^2 \][/tex]
Now divide the potential energy by this product:
[tex]\[ m = \frac{235,200 \, \text{J}}{294 \, \text{m}^2/\text{s}^2} \][/tex]
Finally, compute the division:
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the coaster is:
[tex]\[ 800 \, \text{kg} \][/tex]
Thus, the correct answer is:
[tex]\[ 800 \, \text{kg} \][/tex]
