Mary and Sally are in a foot race (see the figure). When Mary is 22 m from the f

Question

Mary and Sally are in a foot race (see the figure). When Mary is 22 m from the finish line, she has a speed of4.0 m/sand is 5.0 mbehind Sally, who has a speed of5.0 m/s. Sally thinks she has an easy win and so, during the remaining portion of the race, decelerates at a constant rate of 0.32m/s2 to the finish line.

What constant acceleration does Mary now need during the remaining portion of the race, if she wishes to cross the finish line side-by-side with Sally?

Mary and Sally are in a foot race (see the figure). When Mary is 22 m from the finish line, she has a speed of4.0 m/s and is 5.0 m behind Sally, who has a speed of5.0 m/s. Sally thinks she has an easy win and so, during the remaining portion of the race, decelerates at a constant rate of 0.32m/s2 to the finish line. What constant acceleration does Mary now need during the remaining portion of the race, if she wishes to cross the finish line side-by-side with Sally?

Explanation / Answer

let mary needs an acceleration of a m/s^2.

then if time taken by both to reach the finish point is t,

then 5*t-0.5*0.32*t^2=22-5

t=3.88 sec

so for mary:

4*3.88+0.5*a*3.88^2=22

so a=0.86 m/s^2

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