Solving Collision Question: Find Initial Velocities of Cars

[~angel~]

Sorry about this but I don't have a picture, but it is of two cars, one traveling north, the other traveling east, and they collide completely inelastically. The mass of the car traveling east is 950kg, and the mass of the car traveling north is 1900kg. Their final combined velocity is 16m/s, at an angle of 24 degrees east of north. What is each cars' initial velocity?

I worked out an equation for the final momentum, using vectors:

(950v_1)^2 + (1900v_2)^2 = 45600^2

but I don't know how to solve it.

Please help.

Thank you.

 

[TenaliRaman]

~angel~,
You might like to post ur complete working.
I have not done any calculations yet, but one look at your equation suggests to me that something is wrong.

If u post ur working, it would be easier to iron out your problems.

-- AI
P.S -> I believe ur working is wrong because i think u should have got two equations which u need to solve simultaneously. Ofcourse, this is my knee jerk reaction, so its better to see ur working before making any more comments.

 

[~angel~]

I can't get any further than that. I'm completely lost and I don't know what I've done wrong.

This is not an assignment from mastering physics or anything, it's just a question from University Physics (Y&F) that I don't exactly understand. I thought that you're menat to use vectors to solve the equation. Sorry about this.

 

[HallsofIvy]

Your problem is that you have only one equation for 2 unknown speeds which, of course, cannot be solved! The reason you have only one equation is that you are only looking at the magnitude of the momentum when, in fact, momentum is a vector quantity. You need to look at the individual components.

Car 1 is 950 kg and moving east so we can write its velocity vector (v₁,0) and its momentum (950v₁,0).
Car 2 is 1900 kg and is moving north so we can write its velocity vector (0,v₂) and its momentum (0,1900v₂)


The total momentum, before the collision, is (950v₁,1900v₂).

After the collision, since it is "completely inelastic", the two cars move as a single
1900+ 950= 2850 kg mass at "16m/s, at an angle of 24 degrees east of north". Drawing a right triangle representing that, we see that we can write the velocity vector as (16 sin(24), 16 cos(24)) and so the momentum vector is (2850*16 sin(24), 2850*16 cos(24))= (45600 sin(24), 45600 cos(24)).

"Conservation of momentum" requires (950v₁,1900v₂)= (45600 sin(24), 45600 cos(24)) or v₁= 45600 sin(24) and 1900v₂= 45600 cos(24).

Those should be easy to solve.

 

[~angel~]

I understood that I couldn't solve the equation I found =P

Thanks for your help. =)