When will two football players collide?

[rexorsist]

This is Grade 11 Physics. I don't want the answer, I just want to know how to do it:

Two football players separated by 42 m run directly toward each other. Football player #1 starts from rest and accelerates at 2.4 m/s2 [E], and football player #2 moves uniformly at 5.4 m/s [W].

(a) How long does it take for the players to collide?
b)How far does each player move?

I know I have to use on of the 5 motion equations, I just don't know which one since I have no clue on how to handle opposite motions.

I've tried drawing diagrams and really want to avoid using a quadratic equation since my teacher dislikes it. Any other ways?

If a quadratic equation is the easiest way to get the answer, then how would I be able to use it?

 

[NascentOxygen]

Hi rexorsist! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

So you know the equations of motion, good. So write them all down, and for each variable in each equation, place a tick or a cross above it, according to whether or not you are given a value for it in the specifications. Then stand back and examine what you have, and compare with what you'd like to calculate.

You also know that the two runners travel for equal durations here, call that t.

You also know something about the distances traveled here. What relation can you state to show how the distance covered by one runner is related to the distance covered by the other runner? Remember, they both run for the same amount of time, t.

If the solution requires that you must solve a quadratic, then so be it. Let the chips fall where they may!

 

[rexorsist]

I could state a variable, like x, for the distance covered by runner 1, and say that the distance covered by runner 2 is 42m-x.

Is that somewhat on the right track?

Thanks for helping by the way! Means a lot.

 

[NascentOxygen]

I could state a variable, like x, for the distance covered by runner 1, and say that the distance covered by runner 2 is 42m-x.

Is that somewhat on the right track?

That's exactly what I mean.

So now you can form equations of motion in terms of t and x. Do this for each runner. See whether you can get it down to 2 equations in 2 unknowns. Then the rest will be easy--just mathematical manipulation.