Answer :
Final answer:
The average power output of a quarterback who accelerates a 0.42 kg football from rest to 24 m/s in 0.08 s is approximately 1512 watts, or about 2.03 horsepower.
Explanation:
The question asks us to calculate the average power output of a quarterback who accelerates a 0.42 kg football from rest to 24 m/s in 0.08 s. To find the power, we can first calculate the work done on the ball and then divide it by the time during which the work was done.
The work done can be found using the formula:
Work = ½ * mass * (final velocity)^2 - ½ * mass * (initial velocity)^2
Since the initial velocity is 0 (the ball starts from rest), the work done simplifies to:
Work = ½ * 0.42 kg * (24 m/s)^2
Work = 120.96 J
Now, we can find the power by dividing the work by the time:
Power = Work / Time
Power = 120.96 J / 0.08 s
Power = 1512 W
To convert watts to horsepower, we use the conversion rate 1 horsepower = 746 watts:
Power in horsepower = 1512 W / 746 W/hp
Power in horsepower ≈ 2.03 hp
Therefore, the average power output during the quarterback's throw is approximately 1512 W or 2.03 hp.
