In a women\'s 100-m race, accelerating uniformly, Laura takes 1.97 s and Healan

Question

In a women's 100-m race, accelerating uniformly, Laura takes 1.97 s and Healan 3.06 s to attain their maximum speeds, which they each maintain for the rest of the race. They cross the finish line simultaneously, both setting a world record of 10.4 s. What is the acceleration of each sprinter? a_Laura = a_Healan Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error, m/s^2 What are their respective maximum speeds v_Laura, max =________m/s v_Healen, max =______m/s Which sprinter is ahead at the 6.45-s mark, and by how much? Is ahead by______m. What is the maximum distance by which Healan is behind Laura?_____At what time does that occur?_______s

Explanation / Answer

laura max speed =v a=v/t 100 = (0.5*a*1.97*1.97) + (1.97*a*8.43 ) a = 5.39 m/s^2 for laura and her max speed = 5.39*1.97 = 10.62 m/s for healan 100 = (0.5*a*3.06*3.06) + (3.06*a*7.34 ) a = 3.68 m/s^2 max speed = 3.68*3.06 = 11.27 m/s c) laura = (0.5*5.39*1.97*1.97) + ( 10.62*4.48) =58.036 healan = (0.5 *3.68*3.06*3.06) +(11.27*3.39)= 55.43 laura ahead by 2.6 for max distance it woould be at time t SL = (0.5*5.39*1.97*1.97) + ( 10.62*(t-1.97) ) Sh = (0.5*3.68*3.06*3.06) + ( 11.27*(t-3.06) ) SL -Sh should be max at t = 3.06 it will occur and maximum distance = 22.02

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