The athlete Emily Davis won the 100 m sprint gold medal at London Olympic 2012 setting a new Olympic record of 10.54 s . Assume that she achieved her maximum speed in a very short time and subsequently ran the race with that speed till she crossed the line. Take her mass to be 50 kg . Assuming that the track, the wind etc. offered an average resistance of one tenth of her weight, determine the power Emily Davis had t

Step-by-step solution

Given distance s = 100 m and time t = 10.54 s . Since the maximum speed is achieved in a very short time, the uniform speed of the athlete is: v = s t = 100 10.54 m/s The average resistance force offered by the track and wind is one-tenth of her weight. Taking g = 9.8 m/s ^2 : F = 1 10 mg = 1 10 50 9.8 = 49 N To maintain a uniform speed, the athlete must exert a force equal to the resistance force. The power exerted by the athlete is: P = F v = 49 100 10.54 P = 4900 10.54 464.9 W Rounding to the nearest integer giv