I think ##\theta##s are angular displacement, see
Yes.
If ##\boldsymbol{v}_{2i} // \vec{OO'}## and ##\Delta\boldsymbol{v}_2 // \vec{OO'}##,
then ##\boldsymbol{v}_{2f} // \boldsymbol{v}_{2i} // \vec{OO'}##, and so on.
You guys can not see my replies or something?
@Jazz
No friction, and the ##\boldsymbol{F}## through the centers, so ##\theta##s are all constant.
The unknown four variables are ##\boldsymbol{v1_f}## and ##\boldsymbol{v2_f}##, due to 2D problem.
Now we find the other equation
##\boldsymbol{F} //...
Follow you, at last you got a equation by two unknown variables, so you get a relation but cann't solve it.
Then you should find another equation for resolving it.
The forces during collision along the orientation of the line through the centers, the impulse during collision is olong this orientation, so the puck 2 should move along the opposite orientation of ##\boldsymbol{v_2}##.
Plus this, you may completely solve this problem.
There is an error in the measurements of R_1 and R_2 of \Delta R_1 and \Delta R_2 respectively.
It is correct that \frac{\Delta R}{R^2}=\frac{\Delta R_1}{{R_1}^2}+\frac{\Delta R_2}{{R_2}^2}
At what distance from the center of the Earth is the force due to the Earth twice the magnitude of the force due to the Moon?
the force due to Earth and the force due to the Moon, what do they act on?