Suppose you are carrying a ball and running at constant speed, and wish to throw the ball and catch it as it comes back down. neglecting air resistance, should you (a) throw the ball at an angle of about 45° above the horizontal and maintain the same speed, (b) throw the ball straight up in the air and slow down to catch it, or (c) throw the ball straight up in the air and maintain the same speed?

c)

Explanation:

You should throw the ball straight up in the air and maintain the same speed. This was explained by Galileo when thinking what would happen if an object was thrown from the mast of a ship.

Neglecting air resistance, the ball would keep its horizontal velocity, which is the same as yours since it departed from you when moving. Movement on both directions is independent, on the horizontal the ball keeps moving at constant speed while on the vertical it performs a free fall.

since you're a real machine, your ama is always less than your ima, because you can never totally eliminate friction.