College

What is the potential energy of a 25 kg bicycle resting at the top of a hill 3 m high?

(Formula: [tex]PE = mgh[/tex])

A. 75 J
B. 735 J
C. 245 J
D. 37.8 J

Answer :

To find the potential energy of the bicycle resting at the top of the hill, we use the formula:

[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]

where:
- [tex]\( m \)[/tex] is the mass of the bicycle (25 kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 m/s²,
- [tex]\( h \)[/tex] is the height of the hill (3 m).

Step-by-step calculation:

1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 25 kg
- Gravity ([tex]\( g \)[/tex]) = 9.8 m/s²
- Height ([tex]\( h \)[/tex]) = 3 m

2. Substitute the given values into the formula:
[tex]\[ \text{PE} = 25 \cdot 9.8 \cdot 3 \][/tex]

3. Perform the multiplication:
[tex]\[ 25 \cdot 9.8 = 245 \][/tex]
[tex]\[ 245 \cdot 3 = 735 \][/tex]

Thus, the potential energy of the bicycle at the top of the hill is 735 joules.

Therefore, the correct answer is 735 J.