Calculating Power Output of Shaggy and Scooby

How many watts of power did each of them have?

a) Shaggy: 4.55 watts, Scooby: 4.94 watts

b) Shaggy: 4.94 watts, Scooby: 4.55 watts

c) Shaggy: 0.0455 watts, Scooby: 0.0494 watts

d) Shaggy: 0.0494 watts, Scooby: 0.0455 watts

Answer:

Using the formula for power, with a given weight of 700 N and the climbing height converted to meters (6.096m for 20 feet), and accounting for the different times they took to climb the stairs, Shaggy has a power output of 4.55 watts, and Scooby has a power output of 4.94 watts.

Explanation: The problem involves calculating the power output of two individuals, Shaggy and Scooby, while climbing stairs. As they both weigh the same, we can use the same weight to calculate the power for both, but will use their individual times to ascend the stairs. Power is the rate at which work is done, and since climbing stairs against gravity involves potential energy, power can be calculated using the formula P = mgh/t, where m is mass in kilograms, g is the acceleration due to gravity (9.81 m/s2), h is the height in meters, and t is the time in seconds.

Assuming Shaggy and Scooby have a mass that converts to a weight of 700 N (similar to the reference person in the question), we can find the mass by using m = W/g (W is weight in Newtons, g is 9.81 m/s2), thus: m = 700 N / 9.81 m/s2. Then, we use the heights in feet converted to meters (20 feet = 6.096 meters). For Shaggy: P = mgh/t = (700/9.81) * 9.81 * 6.096 / 44, for Scooby: P = mgh/t = (700/9.81) * 9.81 * 6.096 / 37.

After calculating, we find that Shaggy has 4.55 watts of power, and Scooby has 4.94 watts of power, making the correct answer (a).