What if they deflect one object that hits another object that then hits the Earth?
If you want to traslate motion and change the vector you have to hit at the center of mass, otherwise it spins. Sounds low probaility of sucess.
I'd think it would have to be a set of thrusters coordinated to move the object in a predictable manner.
The experiment sounds like an exercise in Newtonian mechanics.
The chance of deflecting one object into another to cause it to hit is minuscule. There are two problems with thrusters: First, you have to match orbits with the target first--unless we have a long lead time that very well might be impossible. Second, they are an inefficient use of your launch mass. You will get more deflection per pound launched by ramming.
Anyway, if there is a seriously threatening object out there the real answer is neither of these. Instead, nuclear-tipped interceptors, fused for standoff detonation. Keep the warheads small enough you don't risk disrupting the target if it turns out to be a pile of gravel. The essence of an Orion drive.