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Balsam

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## Homework Statement

Two football players separated by 42m run directly toward each other. Football player 1 starts from rest and accelerates at 2.4m/s^2, and football player 2 moves uniformly at 5.4m/s.

a) How long does it take for the two players to collide?

b) how far does each player move?

c) How fast is football player 1 moving when the players collide?

For part a- player 1: displacement=42m, a=2.4m/s^2, vi=0m/s.

Player 2: vi=vf=5.4m/s, displacement=42m

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## Homework Equations

I'm only at part a: For player 1, I used the eqn. displacement=vi(t)+1/2a(t)^2

For player 2, I used displacement= (vf+vi/2)t.

## The Attempt at a Solution

I plugged in all known values for both players. I tried this twice- the first time, I plugged in the displacement for each player. The second time, I did not. But, for both attempts, I set the 2 equations equal to each other, moved all variables over to one side of the equals sign, setting the equation equal to 0. Then, I used the quadratic formula and solved for time. I got the same answer both times, 4.5seconds. But, the correct answer is 4.1s. I have the solution for this problem, but it's very confusing. What did I do wrong?

I would type up all of my work, but it's over a page long and would look very confusing/messy if I tried to type itHere's what I did:

player 1: displacement=o(t)+1/2(2.4m/s^2)t^2

displacement=1.2m/s t^2Player2: d=5.4m/s(t)

Then, I set the 2 equations equal to each other:

5.4m/s^2

(t)=1.2m/s(t)^2

I moved all terms over to one side of the equals sign: 1.2m/s

(t)^2-5.4m/s^2(t)=0

Then, I used the quadratic formula to solve for t.

x=5.4+√29.16/2.4

x1=4.5 seconds. x2=0seconds

Therefore, time=4.5seconds. But, the correct answer is 4.1seconds.

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