Elastic collision. to find values

[shin777]

Ok.. So basically 100kg object V100 is coming from left to right at 20m/s and 50kg object V50 is coming from right to left at 35m/s and make collision. They get pushed away like on picture.
I need to find V50 and V100 but from the looks of it, I need to find angle theta to find an answer. How do I find angle theta? It looks like I can use sin^2 + cos^2 = 1 but I just can't put it together. Need some help. :)

 

[darkxponent]

The equation formed for momentum is not correct. You lack some concept i guess. You are not using the LAW OF CONSERVATION OF MOMENTUM Correctly.

HINT: This is a two dimension collission, so the momentum would be conserved in both dimensions

 

[shin777]

Can you be more specific and give me correct equation then? I used exact same equations that my instructor used except the one I did in class didn't have bounce off angle of 30 degree and theta.

 

[gneill]

You have written an expression for the conservation of momentum in the x-direction. But momentum is also conserved (independently) in the y-direction. So you can write another equation expressing that conservation. That will give you three equations in three unknowns (1: conservation of KE in an elastic collision; 2: conservation of momentum in x-direction; 3: conservation of momentum in y-direction, and unknowns V₅₀, V₁₀₀ and θ).

 

[shin777]

I am sorry but I still don't get it. If the angle wasn't presented, I can solve this but with these angles, I just don't know what to do anymore. I can get another equation which is

2(V100)^2 + (V50)^2 = 3250 but I need to find out value for V100 or V50 to solve it and I can't figure out how coz of angle 30 and theta. :(

 

[gneill]

I am sorry but I still don't get it. If the angle wasn't presented, I can solve this but with these angles, I just don't know what to do anymore. I can get another equation which is

2(V100)^2 + (V50)^2 = 3250 but I need to find out value for V100 or V50 to solve it and I can't figure out how coz of angle 30 and theta. :(

Write a conservation of momentum equation for the y-direction. What's the initial momentum in the y-direction?

 

[shin777]

I really don't understand anything anymore. Can somebody please show me how it's done? I am on this for almost 2 hours now and getting nowhere. I really don't understand look up equations and stuff because this class I am taking don't even use a book but just bunch of printed out papers that only has problems written without clear explanation or answers. I take notes from what my instructor writes on board and anything different from the ones he does in class, I can't seem to solve. If it's something he does in class just with different numbers, no problem but problem like this that adds extra element without telling me how to do, I have no idea. I would've gone to see tutor if I had time to visit them but my schedules are full. :(

 

[haruspex]

The replies you've already had are pretty clear - don't know if I can explain it any better, but here goes.
Do you understand that linear momentum is a vector, so conservation of momentum in two dimensions gives you two equations - one in the 'x' direction and one in the 'y' direction?
You have written out an equation for conservation of momentum in the x direction (but it's wrong - you've used sin of theta, which is the velocity in the y direction). Correct that, and write another equation for the y direction. You will then have enough equations to solve the problem.