Calculating Momentum & Velocity After Football Collision

[domyy]

Homework Statement

Two football players collide at an angle of 90 degree and stick together after the collision. Before the collision, player A (m= 125kg) had a speed of 4m/s and player B (m=100kg) had a speed of 5m/s.

1)Calculate the total momentum of the players and the final velocity they had after the collision.

2)Calculate the angle a between the direction player A had before and after the collision. (hint: use tan a=Pa/Pb ).

Homework Equations

I believe:

a^2 + b^2 = c^2

p=m/v

v=v/m

The Attempt at a Solution

To find total momentum, I first calculated momentum for each player:

Player A = 125kg divided by 4m/s = 31.25 kg. m/s
Player B = 100kg divided by 5m/s = 20 kg. m/s

Pt^2 = (20)^2 + (31.25)^2 = 400 + 977 = +/- 37.

To find vf = p/m = 37/125+100 (total mass) = 0.16m/s.

What do you guys think?

 

[pymn_nzr]

helllllooo!

 

[domyy]

Hello!
Thank you for helping but it´s not completely clear to me.
I calculated pt = 1000 but I am just confused with how I am going to find cos(theta) and sin(theta).

For cos= c/b and sin=a/c, but how do I get the values for a, b and c?
Would A equal momentum for player A = 500, for instance?

I am sorry but I am still confused about how I am going to calculate this.

 

[domyy]

Anyone?

 

[domyy]

Please, I need someone to help me with it.

 

[tal444]

Player A = 125kg divided by 4m/s = 31.25 kg. m/s
Player B = 100kg divided by 5m/s = 20 kg. m/s

Remember, momentum formula is this: P=mv

helllllooo!

Your solution makes absolutely no sense. Also, we are forbidden to post complete solutions.

Try this diagram. The red line is the overall momentum after the collision, and θ is the angle you are looking for in part 2.

 

[domyy]

Hi Tal444 !

So, the drawing you have is what I had imagined. That´s why I used the Pythagoras' theorem to calculate total momentum.

I am sorry, I keep writing p=m/v instead of p=mv.

Is the following accurate:

I am trying to calculate total momentum:

Pa = 125x4 =500kg.m/s
Pb = 100x5 = 500kg.m/s

Pt^2 = (500)^2 + (500)^2 = +/- 707

Does that make sense?

 

[tal444]

Yes, other than the fact that your momentum won't be negative in this case. Now, what's next?

 

[domyy]

Now I should calculate vf = p/m = 707/125+100 (total mass) = 3.14 m/s.

 

[domyy]

It won't be negative because they are both going toward the same direction, right?

 

[tal444]

Yes, your velocity is correct. And yes, it won't be negative because they are not opposing momentums. And now I need to go to sleep :zzz:. You're almost done, all you need to do is to find the angle now, and that should be a piece of cake for you.

 

[domyy]

Thank you so much! :)

 

[domyy]

i know you said it should be easy to answer the last question, but would 1 make any sense?
because if to find tan(a) = pa/pb then, the answer would be 500/500 = 1

 

[domyy]

what do you mean?

 

[tal444]

Yes, tan(a) does equal 1, but you're not looking for tan(a). You're looking for a. What does tan^-1 give?

 

[domyy]

Oh I am confused...

 

[domyy]

i got it! 45