Question

select the correct answer from the drop - down menu. whats the kinetic energy of the roller coaster at the top and bottom of the hill? use $ke=\frac{1}{2}mv^{2}$. a roller coaster car has a mass 100 kilograms. at the top of a hill, its moving at a speed of 3 meters/second. after reaching the bottom of the hill, its speed doubles. the cars kinetic energy at the bottom is its kinetic energy at the top. the car has joules of kinetic energy at the bottom of the hill.

Explanation:

Step1: Calculate kinetic - energy at the top

Given $m = 100$ kg, $v_{top}=3$ m/s. Using the formula $KE=\frac{1}{2}mv^{2}$, we have $KE_{top}=\frac{1}{2}\times100\times3^{2}$.
$KE_{top}=\frac{1}{2}\times100\times9 = 450$ J.

Step2: Calculate speed at the bottom

The speed at the bottom $v_{bottom}=2\times v_{top}=2\times3 = 6$ m/s.

Step3: Calculate kinetic - energy at the bottom

Using the formula $KE=\frac{1}{2}mv^{2}$ with $m = 100$ kg and $v_{bottom}=6$ m/s, we get $KE_{bottom}=\frac{1}{2}\times100\times6^{2}$.
$KE_{bottom}=\frac{1}{2}\times100\times36=1800$ J.

Step4: Compare kinetic - energies

To find the ratio of $KE_{bottom}$ to $KE_{top}$, we calculate $\frac{KE_{bottom}}{KE_{top}}=\frac{1800}{450}=4$. So the car's kinetic energy at the bottom is 4 times its kinetic energy at the top.

Answer:

The car's kinetic energy at the bottom is 4 times its kinetic energy at the top. The car has 1800 joules of kinetic energy at the bottom of the hill.