Question

A 40 kg dog is sitting on top of a hillside and has a potential energy of 1,568 J. What is the height of the hillside? (Formula: PE = mgh)

3.9 m
4.0 m
39.2 m
40.0 m

Answer 1

To find the height of the hillside, we can use the formula for potential energy (PE):

\[
PE = mgh
\]

Where:
- \( PE \) is the potential energy (in joules),
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( h \) is the height (in meters).

We are given:
- \( PE = 1568 \, \text{J} \)
- \( m = 40 \, \text{kg} \)

We can rearrange the equation to solve for height \( h \):

\[
h = \frac{PE}{mg}
\]

Now, substituting the known values:

\[
h = \frac{1568 \, \text{J}}{40 \, \text{kg} \times 9.8 \, \text{m/s}^2}
\]

Calculating \( mg \):

\[
mg = 40 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 392 \, \text{N}
\]

Now, substituting \( mg \) back into the equation for \( h \):

\[
h = \frac{1568 \, \text{J}}{392 \, \text{N}} = 4.0 \, \text{m}
\]

Thus, the height of the hillside is:

\[
\boxed{4.0 \, \text{m}}
\]