Question

time (s) kinetic energy (j) 0 0 1 1 2 4 3 9 determine the potential energy the ball has for each second of its descent based on its total and kinetic energy values. plot the points on the coordinate grid.

Explanation:

Step1: Recall energy - conservation formula

The total mechanical energy $E$ is conserved, and $E = PE+KE$, where $PE$ is potential energy and $KE$ is kinetic energy. Assume the total mechanical energy at the start is the maximum potential energy (since $KE = 0$ at $t = 0$). At $t=0$, $E=PE + 0=0$, so the total mechanical energy $E = 0$.

Step2: Calculate potential energy at $t = 1$ s

Using $PE=E - KE$, when $t = 1$ s and $KE = 1$ J, $PE=0 - 1=- 1$ J.

Step3: Calculate potential energy at $t = 2$ s

When $t = 2$ s and $KE = 4$ J, $PE=0 - 4=-4$ J.

Step4: Calculate potential energy at $t = 3$ s

When $t = 3$ s and $KE = 9$ J, $PE=0 - 9=-9$ J.

Answer:

Time (s)	Potential Energy (J)
1	- 1
2	- 4
3	- 9