Kinematics problem-finding acceleration

[life is maths]

Homework Statement

Hi everyone! This is my homework question, an easy one, but I cannot find my mistake. Any help will be greatly appreciated.

Mary and Sally are in a foot race. When Mary is 22 m/s from the finish line, she has a speed of 4.0 m/s and is 5.0 m behind Sally, who has a speed of 5.0 m/s. During the remaining portion of the race, Sally decelerates at a constant rate of 0.48 m/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?

Homework Equations

The Attempt at a Solution

(The final velocity of Sally)=V_sf²
(The initial velocity of Sally)=V_si²
V_sf²:V_si²-2ax
V_sf²=5²-2*0.48*17
which is 3 m/s.
V_sf=V_si+at
3=5-0.48t
t=4.16s

They should finish the race at the same time, so this is also the time in which Mary ran 17 m.

X=V_ot+1/2at²
22=4*4.16+a*(4.16)²
5=2.08*4.16*a
and a=0.60 m/s²

This is an internet assignment and the program says this result is false.
Is there a mistake here? What do I do wrong? Thanks for any help :)

 

[PeterO]

Homework Statement

Hi everyone! This is my homework question, an easy one, but I cannot find my mistake. Any help will be greatly appreciated.

Mary and Sally are in a foot race. When Mary is 22 m/s from the finish line, she has a speed of 4.0 m/s and is 5.0 m behind Sally, who has a speed of 5.0 m/s. During the remaining portion of the race, Sally decelerates at a constant rate of 0.48 m/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?

Homework Equations

The Attempt at a Solution

(The final velocity of Sally)=V_sf²
(The initial velocity of Sally)=V_si²
V_sf²:V_si²-2ax
V_sf²=5²-2*0.48*17
which is 3 m/s.
V_sf=V_si+at
3=5-0.48t
t=4.16s

They should finish the race at the same time, so this is also the time in which Mary ran 17 m.

X=V_ot+1/2at²
22=4*4.16+a*(4.16)²
5=2.08*4.16*a
and a=0.60 m/s²

This is an internet assignment and the program says this result is false.
Is there a mistake here? What do I do wrong? Thanks for any help :)

Homework Statement

Homework Equations

The Attempt at a Solution

Your final velocity of 3 m/s is 2.946... rounded off.
Not sure you can round off like that during the calculations.

EDIT: and also Mary had to run 22m. ( she was 5m behind)

 

[Doc Al]

Be careful about rounding off your intermediate calculations. For example, don't round off Sally's final speed to 3 m/s--that introduces errors in all subsequent calculations.

 

[life is maths]

I did not round off the velocity of Sally, and this time I have t=4.375 s. When I do calculations according to the new value of t, I find the acceleration of Mary as 0.47 m/s^2. I still cannot figure out my mistake, and I used my last chance to answer it. Anyways, this question is a pain in the neck for me for a week.

My mistake that Mary ran 17 m, but I didn't do my calculations according to this mistake.
Thanks for your help :)

 

[Doc Al]

I did not round off the velocity of Sally, and this time I have t=4.375 s.

I got 4.279 s.

 

[life is maths]

I got 4.279 s.

That's true! I have no idea how I could find 4.375 s.

Then

22=4t+1/2at²
22-17.116=9.154a
4.884=9.154a
a=0.53m/s²

I should have been more careful with my calculations and rounding off... I've lost 20 points already, but at least I could solve it. Thanks a lot for your help, Doc Al :)