Solve the following :

Question:

The US athlete Florence Griffith-Joyner won the $100 \mathrm{~m}$ sprint gold medal at Seol Olympic 1988 setting a new Olympic record of $10.54 \mathrm{~s}$. Assume that she achieved her maximum speed in a very short-time and then ran the race with that speed till she crossed the line. Take her mass to be $50 \mathrm{~kg}$. (a) Calculate the kinetic energy of Griffith-Joyner at her full speed. (b) Assuming that the track, the wind etc. offered an average resistance of one tenth of her weight, calculate the work done by the resistance during the run. (c) What power Griffith-Joyner had to exert to maintain uniform speed?

Solution:

(a) $v=\frac{\stackrel{\mathrm{d}}{t}}{\mathrm{t}}=100 / 10.54 \mathrm{~m} / \mathrm{s}$

K.E. $=\frac{1}{2} \mathrm{mv}^{2}=\frac{1}{2} \times 50 \times 9.487^{2}$

K.E. $=2250 \mathrm{~J}$

(b) Weight $=\mathrm{mg}=50 \times 9.8=-490 \mathrm{~J}$

and work done

$W=-R d=\frac{-\mathrm{mg}}{10} \times d=\frac{-490 \times 100}{10}$

(c) Power $P=\frac{w}{t}=\frac{4900}{10.54}$

$P=465 W$

$W=-4900 \mathrm{~J}$

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