Elastic collision/ momentum question w/ conservation of energy

[mjmontgo]

Homework Statement

In deep space a 7.0 kg rubber ball moving along the x-axis with a speed of 20 m/s collides ELASTICALLY with another ball of mass = 25 kg. After the collision the 7.0kg rubber ball's velocity is directed in the positive y axis. Find the final speed of the 7 kg ball, as well as the VELOCITY of the 25 kg ball (speed and direction)

Homework Equations

m₁v₁= m₁v_1f+m₂v_2f

1/2m₁v₁²= 1/2m₁v_1f² +1/2m₂v_2f²

The Attempt at a Solution

so i know that because the smaller mass is afterwards directed in the positive y direction, that all of its x momentum is transferred to the bigger mass. I've found a velocity for the x component of the bigger mass, however I am stucking finding the y component, which in turn would give me the over all final velocity, which i can use to calculate the angle as well as the final speed of the smaller mass. Would be greatly appreciated if someone could point out the extra equation I am missing. Basically what i have so far boils down to these equations:

m₁v_1x= m₂v2_finalx and i work out the x component of the larger mass to be 140/25 m/s

the other equation i have is for the y direction and that is :
-m₂v_2fy= m₁v_1fy

i know i somhow need to use the energy conservation formula but I am just not seeing it.
Thanks a lot in advance for you help and time guys.

 

[BvU]

You're doing fine. Write out the energy conservation using v² = v_x²+v_y²

 

[mjmontgo]

Ok, so I've rewritten the energy conservation formula and what it comes down to is:

m₁v_1xi²= m₁v_1yf²+m₂v_2xf²+m₂v_2yf²


with some substitution with my known quantities i.e mass and m₂v_2xf=140/25

i get 2016= 7kgv_1yf²+25v_2yf²

which i solve in terms of v_1yf and sub into -m₂v_2fy=m₁v_1yf

but when i calculate the velocity i get a negative answer, which doesn't make sense for v_1yf because we already know from the question that it's moving in the positive y- direction after the collision.

Maybe I'm just making a silly arithmetic error but what i get is:

-sqrt(2016-7kg(v_1yf²))=25kgv_1yf² and you can't take sqrt of a negative obviously?

 

[NascentOxygen]

-m₂v_2fy=m₁v_1yf

From this momentum equation you have one velocity in terms of the other, substitute into your energy equation.

 

[BvU]

Still, your method should work.
2016= 7kgv_1yf²+25v_2yf² is fine. How come I continue with
2016 - 7kgv_1yf² = 25v_2yf² and never find a minus sign ?

Ah, I see, you solve in terms of v₁ means you get v_2,y² = (2016 - 7kgv_1yf²)/25 which has 2 solutions, right ?

And you continue with which one ?
Whatever, don't forget to check your outcome, because I think I'm missing something still.

 

[haruspex]

with some substitution with my known quantities i.e mass and m₂v_2xf=140/25

You mean v_2xf=140/25 m/s, yes?

i get 2016= 7kgv_1yf²+25v_2yf²

which i solve in terms of v_1yf and sub into -m₂v_2fy=m₁v_1yf

-sqrt(2016-7kg(v_1yf²))=25kgv_1yf²

I don't see how you get that last equation. It doesn't make sense dimensionally. Did you mean -(2016-7kg(v_1yf²))=25kgv_1yf²? That would be a sign error somewhere. I suspect you squared -m₁v_1yf/m₂ and left the result as negative.