Solving the Inelastic Collision of 3 Balls

[kk727]

Homework Statement

Ball 1: 3kg, 7 m/s initially
Ball 2: 4kg, V m/s initially
Ball 3: 5kg, 10 m/s initially

Find V if the system collides inelastically and moves off at 2 m/s at 5 degrees above the horizontal.

Homework Equations

p + p = p + p (in both x and y directions)

The Attempt at a Solution

I set up the equations for momentum in both directions (sin and cosine). I ended up with 4v*sinθ = 13.7558 and 4v*cosθ = 50.608. I then solved for θ and got 15.2 degrees and an initial velocity for Ball 2 of 13.11 m/s. I don't believe this is the answer my teacher had in class.

My only question is, when setting up the problem, would you consider the velocity of Ball 3 to be negative? That's how I calculated it. I have no problems with the calculations, just the setting up of the problem. I didn't write all of my work down, but it was something like this:

(sin 15)(7)(3) + (sin θ)(v)(4) + (5)(-10)(sin 20) = (2)(sin5)(12)

And I simplified it, did the same for cosines, solved for θ, and then plugged into solve for V.

Am I way off?

:/

 

[Delphi51]

(sin 15)(7)(3) should be negative, too - the vertical component is down.

 

[kk727]

Thank you! I realized I had my signs all wrong...stupid mistake! I figured it out and got the right answer!