Select the correct answer from the drop-down menu.

What is the kinetic energy of the roller coaster at the top and bottom of the hill? Use [tex]KE = \frac{1}{2} mv^2[/tex].

A kiddie roller coaster car has a mass of 100 kilograms. At the top of a hill, it's moving at a speed of 3 meters per second. After reaching the bottom of the hill, its speed doubles.

- The car's kinetic energy at the bottom is [tex]\square[/tex] joules.
- The car's kinetic energy at the top is [tex]\square[/tex] joules.



Answer :

Sure, let's carefully detail the steps required to solve the problem and then fill out the appropriate selections in the drop-down menu.

1. Understanding the Problem:
- Mass of the roller coaster car, \( m \), is 100 kilograms.
- Speed at the top of the hill, \( v_{\text{top}} \), is 3 meters/second.
- Speed at the bottom of the hill, \( v_{\text{bottom}} \), is double the speed at the top. Therefore, \( v_{\text{bottom}} = 2 \times 3 = 6 \) meters/second.

2. Kinetic Energy Calculation at the Top of the Hill:
- The formula for kinetic energy is \( KE = \frac{1}{2} m v^2 \).
- Substituting the values for the top of the hill:
[tex]\[ KE_{\text{top}} = \frac{1}{2} \times 100 \times 3^2 = \frac{1}{2} \times 100 \times 9 = 50 \times 9 = 450 \text{ joules} \][/tex]

3. Kinetic Energy Calculation at the Bottom of the Hill:
- Using the same kinetic energy formula for the bottom:
[tex]\[ KE_{\text{bottom}} = \frac{1}{2} \times 100 \times 6^2 = \frac{1}{2} \times 100 \times 36 = 50 \times 36 = 1800 \text{ joules} \][/tex]

4. Filling in the Drop-down Menu:
- Kinetic energy at the bottom of the hill is \( 1800 \text{ joules} \).
- Kinetic energy at the top of the hill is \( 450 \text{ joules} \).

So, the car's kinetic energy at the bottom is [tex]\( \boxed{1800} \)[/tex] joules of kinetic energy at the bottom of the hill. The car has [tex]\( \boxed{450} \)[/tex] joules of kinetic energy at the top.