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 = m/s^2 a_Healan = m/s^2 What are their respective maximum speeds V_Laura,max = m/s V_Healan,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? Your response differs from the correct answer by more than 10%. Double check your calculations, m At what time does that occur? Your response differs from the correct answer by more than 100%. s

Explanation / Answer

Distance covered = (1/2)at^2 + (at)(10.4 - t)
Where t = time that it takes to accelerate to maximum speed; (at) = maximum speed
So (10.4 - t) = time that they each run at their maximum speed

Laura:
100 m = (1/2)a(1.97)^2 + [(1.97)a](8.43)
100 m = 1.94a + 16.60a
Solve for a: a = 5.393 m/s^2
Vmax = (5.393)(1.97) = 10.625 m/s

So Laura's acceleration is 5.393 m/s^2; Maximum speed = 10.625 m/s


Helen:
100 m = (1/2)a(3.06)^2 + [(3.06)a](7.34)
100 m = 4.68 a + 22.46 a
a = 3.685 m/s^2
Vmax = (3.685 m/s^2)(3.06 s) = 11.274 m/s

So Helen's acceleration is 3.685 m/s^2; Maximum speed is 11.274 m/s

At 6.45 s:
Laura: x = (1/2)(5.393)(1.97)^2 + (4.48)(10.625) = 58.06 m
Helen: x = (1/2)(3.685)(3.06)^2 + (3.39)(11.274) = 55.47 m

So Laura is ahead by 2.60 m

Maximum distance between runners occurs when each has the same velocity
Setting the two equal to each other:

Laura has already reached her maximum speed while Helen is still accelerating so:
10.625 m/s = (3.685)t
Solve for t: t = 2.88 seconds
Distance that each travels during this time:
Laura: (1/2)(5.393)(1.97)^2 + (0.91)(10.625) = 20.133 m
Helen: (1/2)(3.685)(2.88)^2 = 15.282 m
Difference = 4.851 m

So the maximum distance occurs at 2.88 seconds-
Helen is 4.851 m behind

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.