The US athlete Florence Griffith-Joyner won the 100m sprint gold … - Vidyadip

Question

The US athlete Florence Griffith-Joyner won the $100m$ sprint gold medal at Seol Olympic 1988 setting a new Olympic record of $10.54s$. 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 50kg.

Calculate the kinetic energy of Griffith-Joyner at her full speed.
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.
What power GriffithJoyner had to exert to maintain uniform speed?

✓

Answer

$S = 100m, t = 10.54sec, m = 50kg$
The motion can be assumed to be uniform because the time taken for acceleration is minimum.
Speed $\text{v}=\frac{\text{s}}{\text{t}}=9.487\text{m}/\text{s}$
So, K.E. $=\frac{1}{2}\text{mv}^2=2250\text{J}$ Weight = mg = 490J given $\text{R}=\frac{\text{mg}}{10}=49\text{J}$
so, work done against resistance $W_F= -RS = -49 \times 100 = -4900J$
To maintain her uniform speed, she has to exert $4900J$ of energy to over come friction,
$\text{P}=\frac{\text{W}}{\text{t}}$
$=\frac{4900}{10.54}=465\text{W}$

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