can you solve this problem? In a womens 100-m race, accelerating uniformly, Laur

Question

can you solve this problem?

In a womens 100-m race, accelerating uniformly, Laura takes 1.96 s and Healan 3.19 s to attain their maximum speeds, which they each maintain for the rest of the race, the finish line simultaneously, both setting a world record of 10.4 s. What is the acceleration of each sprinter? sLaura = m/s2 aHealan = m/s2 What are their respective maximum speeds VLura, max = m/s vHealan, max = m/s Which spnnter is ahead at the 5.75-s mark, and by how much? is ahead by your response differs from the correctanswer by more than 10%. Double check your calculations. m. What is the maximum distance by which Healan is behind Laura? m At what time does that occur? s

Explanation / Answer

T = 10.4 s
a)VL = aL*1.96

S = 0.5*aL*1.96^2 + vL*(10.4-1.96)

100 = 0.5*aL*1.96^2 + aL*1.96*8.44

aL = 5.41 m/s^2

VH = aH*3.19

S = 0.5*aH*3.19^2 + vL*(10.4-3.19)

100 = 0.5*aH*3.19^2 + aL*3.19*7.21

aH = 3.55 m/s^2

b)VL = aL*1.96 = 10.43 m/s
VH = aH*3.19 = 11.36 m/s

c)
SL = 0.5*5.41*1.96^2 + 10.43*(5.75-1.96) = 49.92 m

SH = 0.5*3.55*3.19^2 + 11.36*(5.75-3.19) = 47.14 m

Laura is ahead by 49.92-47.14 = 2.78 m
d)

at t = 1.96 s

sL = 0.5*5.41*1.96^2 = 10.39 m
SH = 0.5*3.55*1.96^2 = 6.82 m

SL-Sh = 3.57 m

at t = 1.96 s

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