What is the equation for finding the velocities of colliding masses?

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To find the velocities of two colliding vehicles that stick together, momentum conservation must be applied, as kinetic energy is not conserved in perfectly inelastic collisions. The total momentum before the collision can be expressed as two separate equations for the x-components (east-west) and y-components (north-south) of the momentum. The given angle of the combined mass's trajectory after the collision provides additional information to solve for the unknown velocities. It is crucial to focus on momentum rather than kinetic energy for this type of collision. Understanding these principles will aid in determining the pre-collision velocities effectively.
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2 vehicles, one traveling north, the other east, collide and stick together. Their combined mass then slides at a given speed v_3, at a given angle to the east of north.

I also have the masses of the vehicles. I need to find their velocities before crashing. Ignore friction.

So my idea is that the total kinetic energy after the collision is equal to the sum of the kinetic energies of the vehicles before the collision.

I come up with a general equation of the form:

x^2 + y^2 = z, where z is a known number. This of course can't be solved because of the 2 unknowns. So the information I need must lie with the angle given. But I can't figure it out.

Any pointers in the right direction?
 
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Since the vehicles stick together, the collision is perfectly inelastic: KE is not conserved. What is?
 
momentum?
 
Joza said:
momentum?
Absolutely. And since momentum is a vector, set up two equations: one for the x-components (east - west) and another for the y-components (north - south).
 
I haven't read that chapter yet. I'm a bit behind.

I presumed it was energy, that's where I'm up to so far...I'll be there tomoro. Cheers!
 
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