Answer :
To find Robert's power output, we can follow these steps:
1. Identify Known Information:
- Robert's weight is 65 kg.
- The ladder's height is 2.4 meters.
- The time taken to climb the ladder is 11 seconds.
- The acceleration due to gravity (g) is approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex].
2. Calculate the Gravitational Force:
- The force exerted by Robert due to gravity, which is also the weight force, is calculated using the formula:
[tex]\[
\text{Force} = \text{weight} \times g = 65 \, \text{kg} \times 9.8 \, \text{m/s}^2
\][/tex]
- This calculates to 637 N (newtons).
3. Calculate the Work Done:
- Work done is calculated by multiplying the force by the distance (height of the ladder) climbed:
[tex]\[
\text{Work Done} = \text{Force} \times \text{height} = 637 \, \text{N} \times 2.4 \, \text{m}
\][/tex]
- This results in approximately 1528.8 J (joules).
4. Calculate the Power Output:
- Power is the rate at which work is done and is given by the formula:
[tex]\[
\text{Power Output} = \frac{\text{Work Done}}{\text{Time}} = \frac{1528.8 \, \text{J}}{11 \, \text{s}}
\][/tex]
- This results in approximately 138.98 W (watts).
Therefore, Robert's power output is approximately 139 watts. The correct answer from the options given is 139 W.
1. Identify Known Information:
- Robert's weight is 65 kg.
- The ladder's height is 2.4 meters.
- The time taken to climb the ladder is 11 seconds.
- The acceleration due to gravity (g) is approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex].
2. Calculate the Gravitational Force:
- The force exerted by Robert due to gravity, which is also the weight force, is calculated using the formula:
[tex]\[
\text{Force} = \text{weight} \times g = 65 \, \text{kg} \times 9.8 \, \text{m/s}^2
\][/tex]
- This calculates to 637 N (newtons).
3. Calculate the Work Done:
- Work done is calculated by multiplying the force by the distance (height of the ladder) climbed:
[tex]\[
\text{Work Done} = \text{Force} \times \text{height} = 637 \, \text{N} \times 2.4 \, \text{m}
\][/tex]
- This results in approximately 1528.8 J (joules).
4. Calculate the Power Output:
- Power is the rate at which work is done and is given by the formula:
[tex]\[
\text{Power Output} = \frac{\text{Work Done}}{\text{Time}} = \frac{1528.8 \, \text{J}}{11 \, \text{s}}
\][/tex]
- This results in approximately 138.98 W (watts).
Therefore, Robert's power output is approximately 139 watts. The correct answer from the options given is 139 W.
