Abird sitting on the limb of a tree is moving about 30 km/s with respect to the sun. if the bird takes 1 second to drop down to a worm below, the worm would be 30 km downrange from the bird when it reached the ground. this faulty reasoning is best countered with newton's

This faulty reasoning is best countered with Newton's First Law.

Explanation:

Newton's First Law states that every object or body will remain in its state, be it of rest or uniform motion, unless it is affected by a force.

This means that even while sitting, we are all moving at extreme speeds with respect to the Sun, of approximately 30 km/s (yes, including the bird and the worm), but we don't even notice because we are all moving at approximately the same speed, and we aren't being affected by a force strong enough that could change our state of being in said extreme speed with respect to the Sun (that is, unless our Earth suddenly stopped moving around the Sun!).

With that being said, when the bird drops down from the limb of the tree, it moves by "adding" a vertical speed from the tree to the ground, but, in reality, the bird is still moving at 30 km/s in a given axis with respect to the Sun, as well as the worm. Now, since the worm didn't "add" a speed to move away from the bird (or, at least, we assume that's what happened), the bird finally catches the worm.

To sum it all up: Yes, the worm still moves at 30 km/s with respect to the Sun, but the bird moves at the same speed, PLUS a given speed from the tree to the ground that helps it get to the worm.

beta is electron from nucleus

something from nucleus has changed, but charge must be same for cons of charge