Finding initial speeds of two cars from their velocities after collision

[Garvage]

Two cars collide at an intersection. The first car has a mass of 925kg and was traveling north. The second car has a mass of 1075kg and was traveling west. Immediatly after impact, the first car had a velocity of 52km/hr, 310deg, and the second car had a velocity of 40km/hr, 320deg. What was the speed of each car prior to the collision?

Ok.
Is there a velocity formula I can use? One In terms ov V and M?

 

[Garvage]

I think these are the formulas, but I'm not sure.

$$V_{1}=\left(\begin{array}(\underline{(M_{1}+M_{2})}\\(M_{1}-M_{2})\end{array}\right)V_{1}'$$

$$V_{2}=\left(\begin{array}({(2M_{1})}\\\overline{(M_{1}-M_{2})}\end{array}\right)V_{2}'$$

Can anyone help?

 

[christinono]

Yes, those equations are right.

 

[Garvage]

What about getting the right directions? When I use those equations the velocity comes out to be negative. Do I just switch the direction?

 

[christinono]

I think these are the formulas, but I'm not sure.

$$V_{1}=\left(\begin{array}(\underline{(M_{1}+M_{2})}\\(M_{1}-M_{2})\end{array}\right)V_{1}'$$

$$V_{2}=\left(\begin{array}({(2M_{1})}\\\overline{(M_{1}-M_{2})}\end{array}\right)V_{2}'$$

Can anyone help?

Correction:
This formula only applies when a moving ball (A) collides with a stationary ball (B). In this case, you can't use this equation. Rather, you have to use conservation of linear momentum (break down into horiz and vert components). The final and initial horizontal momentum is always conserved. The same goes for the vertical momentum.

 

[Garvage]

So, after I break up the V1' and V2' velocities into horizontal and vertical vectors, can I solve for all four using those formulas? Aslo, what do I do about the velocities being negative since $$M_{1}-M_{2}$$ is negative?

 

[christinono]

So, after I break up the V1' and V2' velocities into horizontal and vertical vectors, can I solve for all four using those formulas? Aslo, what do I do about the velocities being negative since $$M_{1}-M_{2}$$ is negative?

I don't think you can use those formulae at all, since both masses are moving initially. As far as negative velocities, they simply mean the mass is traveling in a negative direction (this can be anywhere, since it depends what you define as the "positive" direction).

 

[Garvage]

Well, that's not good news. Are there any formulae I can use?

 

[christinono]

As far as I know, only

$$Momentum_{horiz/initial}=Momentum_{hor/final}$$

and

$$Momentum_{vert/initial}=Momentum_{vert/final}$$

The only problem is, it seems you're missing one piece of information reguarding the initial speeds.

 

[Garvage]

Yeah, what I am missing is what it's asking me to find.

 

[christinono]

Oh yeah, I read the question again, and you do have enough info. Do you understand how to solve it now?