Aball of mass m collides with a stick with moment of inertia i = βml2 (relative to its center, which is its center of mass). the ball is initially traveling at speed v0 perpendicular to the stick. the ball strikes the stick at a distance d from its center. the collision is elastic.
a). find the resulting translational and rotational speeds of the stick.
b). find the resulting speed of the ball.

Part a)

Part b)

Explanation:

Since the ball and rod is an isolated system and there is no external force on it so by momentum conservation we will have

here we also use angular momentum conservation

so we have

also we know that the collision is elastic collision so we have

so we have

also we know

also we know

so we have

now we have

Part b)

Now we know that speed of the ball after collision is given as

so it is given as

i would say the answer is food.

hope this !