Careful measurements have been made of Olympic sprinters in the 100-meter dash.
ID: 1658936 • Letter: C
Question
Careful measurements have been made of Olympic sprinters in the 100-meter dash. A simple but reasonably accurate model is that a sprinter accelerates at 3.7 m/s2 for 3.37 s, then runs at constant velocity to the finish line.
(a) What is the race time for a sprinter who follows this model? (Enter your answer to at least two decimal places.)
(b) A sprinter could run a faster race by accelerating faster at the beginning, thus reaching top speed sooner. If a sprinter's top speed is the same as in part a, what acceleration would he need to run the 100-meter dash in 9.61 s? m/s2
(c) By what percent did the sprinter need to increase his acceleration in order to decrease his time by 1%?
Explanation / Answer
a] formulating the equation for distance
s = 0.5 a t1^2 + (t-t1)*a*t1
100 = 0.5*3.7*3.37^2 + (t-3.37)*3.7*3.37
t = 9.705 s
b] top speed = 3.7*3.37 m/s
again, 100 = 0.5at1^2 + (9.61 - t1)*3.7*3.37 also t1=3.7*3.37/a
100 = 0.5a*(3.7*3.37/a)^2 + (9.61 - (3.7*3.37/a))*3.7*3.37
a = 3.9208 m/s^2
c) Here we can see that % decrease in time is 1%,.
percentage increase in acceleration = (3.9208-3.7)*100/3.7
= 5.97 %. answer