Answer :
Sure, let's solve the problem step-by-step!
We are given:
- Potential energy ([tex]\(PE\)[/tex]) = [tex]\(235,200 \, \text{J}\)[/tex]
- Height ([tex]\(h\)[/tex]) = [tex]\(30 \, \text{m}\)[/tex]
- Acceleration due to gravity ([tex]\(g\)[/tex]) = [tex]\(9.8 \, \text{m/s}^2\)[/tex]
We need to find the mass ([tex]\(m\)[/tex]) of the roller coaster, using the formula:
[tex]\[ PE = mgh \][/tex]
First, we will rearrange the formula to solve for mass ([tex]\(m\)[/tex]):
[tex]\[ m = \frac{PE}{gh} \][/tex]
Now, we will substitute the given values into the formula:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Next, we calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Then we divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
Performing the division gives:
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is approximately [tex]\(800 \, \text{kg}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{800 \, \text{kg}} \][/tex]
We are given:
- Potential energy ([tex]\(PE\)[/tex]) = [tex]\(235,200 \, \text{J}\)[/tex]
- Height ([tex]\(h\)[/tex]) = [tex]\(30 \, \text{m}\)[/tex]
- Acceleration due to gravity ([tex]\(g\)[/tex]) = [tex]\(9.8 \, \text{m/s}^2\)[/tex]
We need to find the mass ([tex]\(m\)[/tex]) of the roller coaster, using the formula:
[tex]\[ PE = mgh \][/tex]
First, we will rearrange the formula to solve for mass ([tex]\(m\)[/tex]):
[tex]\[ m = \frac{PE}{gh} \][/tex]
Now, we will substitute the given values into the formula:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Next, we calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Then we divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
Performing the division gives:
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is approximately [tex]\(800 \, \text{kg}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{800 \, \text{kg}} \][/tex]
