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Answer :
Final answer:
To convert Maurice Greene's 100-meter sprint time to kilometers per hour using dimensional analysis, we first calculate his speed in meters per second and then convert that to km/h, which rounds to the nearest given option of 36.3 km/h.
Explanation:
To calculate Maurice Greene's speed in kilometers per hour, we can use dimensional analysis to convert his speed from meters per second to kilometers per hour. First, let's find his speed in meters per second.
Speed in meters per second (m/s) = Distance (m) ÷ Time (s)
Speed in m/s = 100 m ÷ 9.87 s = 10.1311 m/s
Now, let's convert this to kilometers per hour.
We know that 1 km = 1000 m and 1 hour = 3600 seconds. Thus, to convert Greene's speed into km/h, we multiply by factors that will cancel out the meters and seconds to leave kilometers and hours.
Speed in km/h = 10.1311 m/s × (1 km / 1000 m) × (3600 s / 1 hour)
Speed in km/h = 36.47196 km/h
When rounded to the nearest tenth, Greene's speed is 36.5 km/h. However, this is not an option in the provided choices. Looking at the options, the closest value and the correct answer is (a) 36.3 km/h.
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