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A 60 kg human sprinter can accelerate from rest to 10 m/s in 2.8 s. During the same time interval, a 31 kg greyhound can go from rest to 20 m/s.

What is the average power output of the human? Average power over a time interval ∆t is ∆E/∆t.
Express your answer to two significant figures and include the appropriate units.
P=______

What is the average power output of the greyhound?
Express your answer to two significant figures and include the appropriate units.
P=______

User Ulugbek
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Final answer:

The average power output of the 60 kg human sprinter is 1071.43 watts (or 1.44 horsepower), and that of the 31 kg greyhound is 2214.29 watts (or 2.97 horsepower), calculated by using the formula for kinetic energy and dividing by the time interval.

Step-by-step explanation:

To find the average power output of the sprinter, we can use the formula for kinetic energy (KE) and the definition of power (P). The kinetic energy of the sprinter can be calculated using the formula KE = 1/2 × mass × (velocity)^2. The sprinter's mass (m) is 60 kg and the final velocity (v) is 10 m/s. The kinetic energy (KE) of the sprinter is therefore KE = 1/2 × 60 kg × (10 m/s)^2 = 3000 J. Since the sprinter reaches this kinetic energy in 2.8 seconds, the average power output can be calculated by dividing the energy by time (P = ΔE/Δt), which gives us P = 3000 J / 2.8 s = 1071.43 W. Converting watts to horsepower (1 HP = 746 W), we get 1071.43 W × (1 HP / 746 W) = 1.44 HP.

The process is similar for the greyhound. The greyhound's mass is 31 kg, and it reaches a final velocity of 20 m/s in the same time interval. Its kinetic energy is KE = 1/2 × 31 kg × (20 m/s)^2 = 6200 J. Dividing this by the time interval gives an average power output of P = 6200 J / 2.8 s = 2214.29 W, which is approximately 2.97 HP.

In conclusion, the average power output of the 60 kg human sprinter is 1071.43 watts (or 1.44 horsepower), and the average power output of the 31 kg greyhound is 2214.29 watts (or 2.97 horsepower).

User Lukewitmer
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