please explain steps clearly. thanks. 4/8 points Previous Answers SerPSET9 2 P08

Question

please explain steps clearly. thanks.

4/8 points Previous Answers SerPSET9 2 P083. My Notes Ask Your Teachen In a women's 100-m race, accelerating uniformly, Laura takes 1.90 s and Healan 3.05 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? Laura 5.58 Hoalan 3.69 m/s (b) What are their respective maximum spe 11.1389 Laura,max Your response is wi thin 10% of the correct value This may be due to round error, or you could have a mistake in error. m/s our calculation carry out a intemediate esu sto e es ou di,t sc un y mis (c) Which sprinter is ahead at the 5.80-s mark, and by how much? Laurais ahead by 1.91 Your response differs from the correct answer by more than 10%. Dauble check your calculations. m (d) What is the maximum distance by which Healan is behind Leura? 5 625 Your response differs from the correct nswer by more than 10%. Double check your calculations, m At what time does that occur? Your response differs from the correct ansner by more than 10%. Double check your calculations. s Need Help? Res

Explanation / Answer

(a) let the acceleration of Laura be al and acceleration of healan be ah.

also, tl = time for which laura accelerate and th = time for which Healen accelerate

for Laura,

100m =( distance covered while accelerating) + ( distance covered at constant speed)

or, 100 = (1/2)al tl2 + al tl(10.4 - tl) = 1.805al + 16.15al = 17.955al (using formula s=ut+at2/2 )

hence, al = 5.569 m/s2

similarly, ah = 3.695 m/s2

(b). the maximum speed of Laura is given by,

Vl = al tl = 5.569 * 1.9 = 10.58 m/s (using formula v=u+at)

similarly, Vh = ah th = 3.695 * 3.05 = 11.26 m/s

(c). Sl = distance covered by Laura in 5.8 s = (1/2)al tl2 + al tl(10.4 - tl)

or, Sl = 0.5 * 5.569* 1.9*1.9 + 5.56 * (5.8 - 1.9) = 10.05 + 41.26 = 51.31 m

similarly,

Sh = distance covered by Heale = 0.5 * 3.695 *3.05*3.05 + 11.26 (5.8 - 3.05) = 17.18 + 30.96 = 48.14m

hence, Laura is ahead by 3.17m after 5.8 s.

(d). The maximum distance Healen will be behind laura at the time Healen attains maximum spped of Laura (i.e. 10.58 m/s)

let t be the time taken by Healen to attain speed of 10.58 m/s (which is maximum speed of Laura)

using formula, v = u + at,

10.58 = 0 + 3.695*t

hence, t = 2.86 s.

distance travelled by Laura in 2.86 s = 0.5*5.569*1.9*1.9 + 10.58*(2.86-1.9) = 10.05 + 10.15 =20.2m

distance travelled by Healen in 2.86 s = 0.5*3.695*2.86*2.86 = 15.11m

therefore, the maximum distance Healen is behind Laura is 5.09 m

the time is 2.86 s.

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