Final answer:
The time taken for a 75 kg person to ascend 44 meters with a power output of 200 J/s is approximately 161.2 seconds.
Step-by-step explanation:
To calculate the time taken for a person to ascend a vertical height using a certain amount of power, we can use the formula for power (P) in terms of work (W) and time (t):
P = W/t, where W is the work done and is given by the formula W = mgh for gravitational potential energy. Here, m is the mass of the person, g is the acceleration due to gravity (approximately 9.81 m/s2), and h is the height ascended. Rearranging for t, we get t = W/P.
In this case, the person's mass (m) is 75 kg, the height (h) is 44 m, and the power output (P) is 200 J/s (which is also 200 W). Substituting these values, we have:
W = 75 kg * 9.81 m/s2 * 44 m = 32,247 J
t = 32,247 J / 200 W = 161.235 s
The time taken for the man to ascend is therefore approximately 161.2 seconds.