To find the power output of the sportsman, we need to follow a series of physical principles and equations to guide us to the correct answer.
1. Determine the Work Done:
The work done by the sportsman can be calculated using the formula for gravitational potential energy, which is:
[tex]\[
\text{Work Done} = \text{mass} \times \text{gravity} \times \text{height}
\][/tex]
Given values:
- Mass ([tex]\(m\)[/tex]) = 70 kg
- Height ([tex]\(h\)[/tex]) = 4.5 m
- Acceleration due to gravity ([tex]\(g\)[/tex]) = 9.8 m/s[tex]\(^2\)[/tex]
Plugging in the values, we get:
[tex]\[
\text{Work Done} = 70\, \text{kg} \times 9.8\, \text{m/s}^2 \times 4.5\, \text{m}
\][/tex]
[tex]\[
\text{Work Done} = 3087\, \text{Joules (J)}
\][/tex]
2. Calculate the Power Output:
Power is the rate at which work is done and is given by the formula:
[tex]\[
\text{Power} = \frac{\text{Work Done}}{\text{Time}}
\][/tex]
Given that the time ([tex]\(t\)[/tex]) is 4 seconds, we have:
[tex]\[
\text{Power} = \frac{3087\, \text{J}}{4\, \text{s}}
\][/tex]
[tex]\[
\text{Power} = 771.75\, \text{Watts (W)}
\][/tex]
3. Determine the Correct Option:
The power output calculated is 771.75 watts. Among the given options, option A is [tex]\(7.7 \times 10^2 W\)[/tex], which is the closest and correctly matches 771.75 W when expressed in scientific notation.
Therefore, the correct answer is:
A. [tex]\(7.7 \times 10^2 \, W\)[/tex]
