Certainly! Let's solve the problem step-by-step.
We are given:
- Mass ([tex]\( m \)[/tex]) of the dog: [tex]\( 40 \, kg \)[/tex]
- Potential energy ([tex]\( PE \)[/tex]): [tex]\( 1568 \, J \)[/tex]
- Acceleration due to gravity ([tex]\( g \)[/tex]): [tex]\( 9.8 \, m/s^2 \)[/tex]
We need to find the height ([tex]\( h \)[/tex]) of the hillside.
The formula for potential energy is:
[tex]\[ PE = mgh \][/tex]
We can rearrange this formula to solve for height ([tex]\( h \)[/tex]):
[tex]\[ h = \frac{PE}{mg} \][/tex]
Let's plug in the values:
[tex]\[ h = \frac{1568 \, J}{40 \, kg \times 9.8 \, m/s^2} \][/tex]
Next, let's simplify the expression:
[tex]\[ h = \frac{1568}{40 \times 9.8} \][/tex]
Now, we compute the denominator first:
[tex]\[ 40 \times 9.8 = 392 \][/tex]
Then, divide the potential energy by this product:
[tex]\[ h = \frac{1568}{392} \][/tex]
Finally:
[tex]\[ h = 4.0 \, m \][/tex]
Therefore, the height of the hillside is:
[tex]\[ \boxed{4.0 \, m} \][/tex]
So, the correct answer is:
[tex]\[ 4.0 \, m \][/tex]
