## Physics Friday 109

Continuing from last week, we consider the speed of the mass M after it undergoes a deflection by the maximum angle  in a collision with an initially stationary mass m<M.

Recalling the circle formed by the possible velocities, with the maximum angle representing the tangent vector, we can use the right triangle to find the velocity.

Specifically, the Pythagorean theorem tells us that
,
so that we see that the smaller the stationary mass m is in proportion to the mass M, the closer the maximum-angle post-collision velocity is to the pre-collision velocity in both direction and magnitude; and as the masses aproach equality, the maximum-angle post-collision speed goes to zero.
Lastly, we can find the speed as a function of the maximum angle via :
.