How fast must a 100 kg object be going in order for it to stop a 200 kg object traveling at 10 km/hr when the two objects collide head on?

Hello!

I suppose that both objects move along the same straight line towards each other with the uniform velocities. Also I suppose that they do not lose energy during the collision (this is called elastic collision).

Denote the first object as with the mass and the second as with the mass Denote the magnitude of the A's speed before the collision as (let it be directed to the right) and the magnitude of the B's speed as (to the left). The speed of after the collision is zero (it stops), the magnitude of the speed of after the collision is I think it will be directed to the left.

Then consider the projection to the line of their movement and use the momentum conservation law:

and the kinetic energy conservation law:

Note the plus and minus signs.

This is the system of equations, the unknowns are and Let's solve it.

The first equation is equivalent to  

the second equation is equivalent to  

Divide the latter by the former and obtain    or   Substitute this to the first equation and obtain

This gives us   or

This is the final formula, and numerically it is   a half of

(you can find by yourself and make sure it is positive, so we guessed its direction correctly)