Question

While skiing in Jackson, Wyoming, your friend Ben (of mass 63.2 kg) started his de- scent down the bunny run. 11.5 m above the bottom of the run. If he started at rest and converted all of his gravitational potential energy into kinetic energy, what is Ben's kinetic energy at the bottom of the bunny run? Use g = 9.8 m/s Answer in units of J.​

Answer 1

Approximately
`7.1 * 10^(3)\; {\rm J}` (given:
`g = 9.8\; {\rm m\cdot s^(-2)}`.)

Step-by-step explanation:

To find the change in the gravitational potential energy (
`\text{GPE}`), use the formula:

`\begin{aligned}& (\text{change in GPE}) \\ &= (\text{mass})\, (g)\, (\text{change in height})\end{aligned}`.

Assume that gravitational field strength
`g` is constant (e.g.,
`g = 9.8\; {\rm m\cdot s^(-2)}`.) For an object of mass
`m`, if the altitude of the object changes by
`\Delta h`, the
`\text{GPE}` of that object would change by
`m\, g\, \Delta h`.

In this question, the mass of Ben is
`m = 63.2\; {\rm kg}`. It is given that
`g = 9.8\; {\rm m\cdot s^(-2)} = 9.8\; {\rm N\cdot kg^(-1)}` and is constant. Since change in the altitude of Ben is
`\Delta h = 11.5\; {\rm m}`, the change in the (
`\text{GPE}`) of Ben would be:

`\begin{aligned} m\, g\, \Delta h &= (63.2\; {\rm kg}) \, (9.8\; {\rm N\cdot kg^(-1)})\, (11.5\; {\rm m}) \\ &\approx 7.1* 10^(3)\; {\rm N\cdot m} = 7.1* 10^(3)\; {\rm J} \end{aligned}`.