Usain Bolt's world-record $100 \mathrm{~m}$ sprint on August 16, 2009, has been analyzed in detail. At the start of the race, the 94.0 $\mathrm{kg}$ Bolt accelerated from rest at a rate of $9.50 \mathrm{~m} / \mathrm{s}^{2}$ for the first $0.890 \mathrm{~s}$, and eventually reached a top speed of $12.4 \mathrm{~m} / \mathrm{s}$ by exerting an average horizontal force of $820 \mathrm{~N}$ against the ground for the entire 9.58 s duration of the race. (a) What was the average horizontal force (in $\mathrm{N}$ ) exerted by Bolt against the ground during the first 0.890 s of the race? $\mathrm{N}$ (b) What was Bolt's speed (in $\mathrm{m} / \mathrm{s}$ ) after the initial acceleration phase? $\mathrm{m} / \mathrm{s}$ (c) What was the power expended by Bolt during the initial acceleration phase? (Give the magnitude of your answer in W.) W (d) It has been shown that, because of his large frame and $65^{\circ}$ height, Bolt experienced significant drag forces during the sprint. To estimate the eneroy lost to drag forces during the race, let's focus on the romaining $9.58 \mathrm{~s}-0.890 \mathrm{~s}=8.69 \mathrm{~s}$ of the race after Bolt's initial burst of acceleration. The drag folce varies with speec, but let's find an average drag force over the last 8.69 s of the race. Model the drag force as a friction force and ind the increase in internal energy of Bolt and the surrounding air in these $8.69 \mathrm{~s}$ as Bolt runs through the air. (Give your answer in 3.) (e) Finally, find the power that Bott must expend just to overcome the drag force and compare it to the result in aart (c). (Give the magnitude of your answer in W.) w.

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