The US athlete Florence Griffith-Joyner won the 100 m sprint gold medal at Seol Olympic 1988 setting a new Olympic record of 10.54 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 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?
Mass of the athlete = m = 50 kg
It is given to assume that she travelled the 100 m distance in 10.54 s with a uniform speed, v
⇒ v = 100/10.54 = 9.48766603 ≈ 9.4877 m/s
(a.) Kinetic energy of Griffith-Joyner at this speed = mv2/2
= 50×9.4877×9.4877×0.5
= 2250.411 ≈ 2250 J
(b.) Force of resistance F = weight of the athlete / 10
= 50 × 9.8 × 0.1
= 49 N
Since, speed is assumed to be a constant, acceleration a =0 m/s2
⇒ Force in the direction of motion or acceleration = ma = 0
Total work done by resistance = Fscosθ
(where θ = angle between resistant force F and displacement s)
= 49 × 100 × cos 180°
= -4900 J
(c.) Power = work done / time for which the work is done
= 4900/10.54
= 464.89 J/s or W
≈ 465 W