To determine Tony's power while doing pushups, we first need to calculate the work done per pushup and the rate at which he does the work (which is tied to his time interval).

However, the problem only gives information about running (speed and mass). Assuming the focus is to derive his mechanical power during pushups, we must make some assumptions about the pushup motion (e.g., lifting his own body weight partially over a certain distance).

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Calculation:

1. Mechanical Work Done in a Pushup

During a pushup, Tony lifts part of his body weight. Let's estimate that he lifts 70% of his body weight (common assumption for pushups) over a vertical displacement of 0.5 meters (a reasonable assumption for the chest-to-arm extension distance). Using this:

$\text{Force exerted by Tony during a pushup} = 0.7 \cdot m \cdot g$

$= 0.7 \cdot 80 \cdot 10 = 560 \, \text{N}$

$\text{Work done per pushup} = \text{Force} \cdot \text{Displacement}$

$= 560 \cdot 0.5 = 280 \, \text{J (joules)}$

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2. Power Output During Pushups

To compute his power, we need his pushup rate (number of pushups per second). Since it's not provided, we'll estimate based on typical fitness scenarios. Assuming Tony does 20 pushups per minute (or 0.33 pushups per second):

$\text{Power} = \text{Work per pushup} \cdot \text{Pushup rate}$

$= 280 \cdot 0.33 = 92.4 \, \text{W (watts)}$

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Final Answer:

Tony’s estimated power output during pushups is approximately:

$\boxed{92.4 \, \text{W}}$

Let me know if you'd like to refine this calculation or explore a different aspect of Tony's workout mechanics!

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Related Questions:

1. How is power related to energy expenditure during exercise?
2. What assumptions were made in calculating Tony’s power output during pushups?
3. How does the running data (100m in 14 seconds) affect power calculations?
4. How would an increase in pushup rate affect Tony's power output?
5. What percentage of the body weight is typically lifted during different exercises?

Tip: Always make reasonable assumptions in physics problems when some variables are unknown, and clearly state them!