499610 In a women\'s 100-m race, accelerating uniformly, Laura takes 1.95 s and

Question

499610 In a women's 100-m race, accelerating uniformly, Laura takes 1.95 s and Healan 3.04 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. (a) What is the acceleration of each sprinter? (b) What are their respective maximum speeds (c) Which sprinter Is ahead at the 6.35-s mark, and by how much? Your response differs from the correct answer by more than 100%. m. (d) What Is the maximum distance by which Healan is behind Laura? m At what time does that occur?

Explanation / Answer

the seperation between laura and healan decreases once laura attains a maximum speed of healan

time taken by laura to reach a speed of vf = 10.8 m/s

vf = aL*t

t = vf/ah = 10.8/3.7 = 2.92 s

distance travelled by healan by t = sh = 0.5*ah*1.95^2 + 10.8*(2.92-1.95)

distance travelled by laura = sL = 0.5*al*t^2

sh - sL = (0.5*5.54*1.95^2)+(10.8*(2.92-1.95)-(0.5*3.7*2.92^2)

maximum seperation = 5.23 m <<----answer

+++++++

time it occurs = 2.92 s <<-----answer

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