In an action-adventure movie, the hero lifts the 89-kg villain straight upward through a distance of 2.0 m in 0.47 s at a constant speed. What power does the hero produce while doing this?
To calculate the power, we need to find the work done by the hero in lifting the villain and then divide it by the time taken. Here's how to do it:
Step 1: Find the work done
The work done (W) is given by the formula:
W = Force × Distance × cos(θ)
In this case, the force required is equal to the weight of the villain, which can be calculated using the formula:
Force = mass × acceleration due to gravity
Force = 89 kg × 9.8 m/s²
Distance = 2.0 m
θ is the angle between the direction of the force and the direction of the displacement. Since the force and displacement are in the same direction (straight upward), θ = 0 degrees and cos(0) = 1.
Putting it all together:
W = (89 kg × 9.8 m/s²) × 2.0 m × 1
Step 2: Calculate the power
Power (P) is given by the formula:
P = Work / Time
In this case, the work done is W from Step 1 and the time taken is given as 0.47 s.
P = W / 0.47 s
Now, you can substitute the value of W from Step 1 and calculate the power by dividing it by 0.47 s.
P = (89 kg × 9.8 m/s² × 2.0 m) / 0.47 s
Simplifying the equation will give you the power produced by the hero while lifting the villain.