(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two cars, both of mass m, collide and stick together. Prior to the collision, one car had been traveling north at speed 2v, while the second was traveling at speed v at an angle [tex]\phi[/tex]south of east (as indicated in the figure). After the collision, the two-car system travels at speed v_{final}at an angle [tex]\theta[/tex] east of north.

Find the speed v_{final}of the joined cars after the collision.

Express your answer in terms of v and [tex]\phi[/tex] .

2. Relevant equations

p=mv

p_{i}=p_{f}

3. The attempt at a solution

first i tried to break this down in terms of its components

in the x direction:

m_{1}v_{1i}cos[tex]\phi[/tex] =(m_{1}+m_{2})V_{final}sin[tex]\theta[/tex]

in the y direction:

m_{1}v_{1}sin[tex]\phi[/tex]+m_{2}2v = (m1+m2)v_{final}cos[tex]\theta[/tex]

Now here is where I am starting to get mixed up. I have both of my components. (They may be wrong so please help me with those equations) Do I just solve both for v_{final}and then square them and take the square root? Any insight is much appreciated.

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# Using conservation of momentum to find final velocity in a collision

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