Question

reflection: at what point(s) does the roller coaster have the most pe? at what point(s) does the roller coaster have roughly equal ke & pe?

Explanation:

Step1: Recall potential - energy formula

The gravitational potential energy formula is $PE = mgh$, where $m$ is mass, $g$ is gravitational acceleration, and $h$ is height. The higher the roller - coaster, the more potential energy it has.

Step2: Determine point of maximum PE

The roller - coaster has the most potential energy at its highest point(s) on the track.

Step3: Recall kinetic - energy formula and energy relationship

The kinetic energy formula is $KE=\frac{1}{2}mv^{2}$, where $m$ is mass and $v$ is velocity. The total mechanical energy $E = KE + PE$. When $KE = PE$, then $E=2KE = 2PE$.

Step4: Find point of equal KE and PE

Assuming total mechanical energy is conserved (neglecting friction etc.), the roller - coaster has roughly equal $KE$ and $PE$ at a point where its height is half of its maximum height (since $PE=mgh$ and $KE$ is related to the loss of $PE$ as it descends). At this mid - height point, half of the initial potential energy has been converted to kinetic energy.

Answer:

1. The roller - coaster has the most PE at its highest point(s) on the track.
2. The roller - coaster has roughly equal KE and PE at a point where its height is approximately half of its maximum height.