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.

 

[HalfLostAndSearching]

To determine when the two football players will collide, we can use the concept of relative motion and the equations of motion. First, we need to determine the initial velocities of both players. Football player #1 starts from rest, so their initial velocity (u1) is 0 m/s. Football player #2 moves uniformly, so their initial velocity (u2) is 5.4 m/s [W].

Next, we need to determine the acceleration of football player #1. We are given that they accelerate at 2.4 m/s2 [E]. However, since we are dealing with opposite motions, we need to take the acceleration of football player #2 into consideration as well. The acceleration of football player #2 is 0 m/s2, since they are moving at a constant velocity. Therefore, the net acceleration of the system is 2.4 m/s2 [E] - 0 m/s2 = 2.4 m/s2 [E].

Now, using the equation of motion s = ut + 1/2at^2, we can determine the time it takes for the players to collide. We know that the final displacement (s) is 42 m, the initial velocity (u) is 5.4 m/s [W], and the acceleration (a) is 2.4 m/s2 [E]. Plugging these values into the equation and solving for t, we get t = 4.5 seconds. This means that it will take 4.5 seconds for the two football players to collide.

To determine how far each player moves, we can use the equation s = ut + 1/2at^2 again. We know that the time (t) is 4.5 seconds, the initial velocity (u) for football player #1 is 0 m/s, and the acceleration (a) is 2.4 m/s2 [E]. Plugging these values into the equation, we get s1 = 0 m + 1/2 (2.4 m/s2) (4.5 s)^2 = 48.6 m. This means that football player #1 will move 48.6 meters before colliding with football player #2.

Similarly, for football player #2, we can use the same equation but with their initial velocity (u) being 5.4 m/s [W]. This gives us s