Answer :
Sure! Let's go through the solution step by step.
We are given that a 40 kg dog is sitting on top of a hillside with a potential energy of 1.56 kJ. We need to find out the height of the hill from these choices: 3.9 m, 4.0 m, 39.2 m, 40.0 m.
Here's the process to solve the problem:
1. Convert Potential Energy: The potential energy is given as 1.56 kJ. Since energy is typically measured in Joules (J) in physics problems, and 1 kJ is equal to 1000 J, we convert this to Joules:
[tex]\[
1.56 \, \text{kJ} = 1560 \, \text{J}
\][/tex]
2. Use the Formula for Potential Energy: The formula for potential energy is:
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
where [tex]\( PE \)[/tex] is the potential energy, [tex]\( m \)[/tex] is the mass, [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]), and [tex]\( h \)[/tex] is the height.
3. Rearrange the Formula to Solve for Height [tex]\( h \)[/tex]:
[tex]\[
h = \frac{PE}{m \cdot g}
\][/tex]
4. Substitute the Values:
- [tex]\( PE = 1560 \, \text{J} \)[/tex]
- [tex]\( m = 40 \, \text{kg} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
So,
[tex]\[
h = \frac{1560}{40 \cdot 9.8}
\][/tex]
5. Calculate the Height:
[tex]\[
h \approx 3.979591836734694
\][/tex]
6. Select the Closest Value from the Options Provided:
The closest value to the calculated height is approximately 3.98 m, which matches the option 3.9 m when rounded.
Therefore, the height of the hill is approximately 3.9 m.
We are given that a 40 kg dog is sitting on top of a hillside with a potential energy of 1.56 kJ. We need to find out the height of the hill from these choices: 3.9 m, 4.0 m, 39.2 m, 40.0 m.
Here's the process to solve the problem:
1. Convert Potential Energy: The potential energy is given as 1.56 kJ. Since energy is typically measured in Joules (J) in physics problems, and 1 kJ is equal to 1000 J, we convert this to Joules:
[tex]\[
1.56 \, \text{kJ} = 1560 \, \text{J}
\][/tex]
2. Use the Formula for Potential Energy: The formula for potential energy is:
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
where [tex]\( PE \)[/tex] is the potential energy, [tex]\( m \)[/tex] is the mass, [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]), and [tex]\( h \)[/tex] is the height.
3. Rearrange the Formula to Solve for Height [tex]\( h \)[/tex]:
[tex]\[
h = \frac{PE}{m \cdot g}
\][/tex]
4. Substitute the Values:
- [tex]\( PE = 1560 \, \text{J} \)[/tex]
- [tex]\( m = 40 \, \text{kg} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
So,
[tex]\[
h = \frac{1560}{40 \cdot 9.8}
\][/tex]
5. Calculate the Height:
[tex]\[
h \approx 3.979591836734694
\][/tex]
6. Select the Closest Value from the Options Provided:
The closest value to the calculated height is approximately 3.98 m, which matches the option 3.9 m when rounded.
Therefore, the height of the hill is approximately 3.9 m.
