Using classical mechanics, a body is projected upwards from the origin at a velocity v than falls to the ground. Ignoring air resistance, it can be shown that the velocity of the ball on impact at the origin is equal in magnitude to the initial velocity v. A bit of a more realistic model. Allow for air resistance for a sphere of a given mass & diameter, with initial velocity v. When the ball falls back to the origin, will the speed be of equal magnitude to the initial velocity? If I take all my calculations from the origin, I can show it is - though I may have made a dodgy assumption doing it this way). If I go to the max high point, reset that as the origin with initial velocity of zero, I get a different (lower value ) answer (my calc's for h max are correct). This goes against my intuition that both values should be equal, I've checked over and over and I'm pretty confident that the calculations (second method) are correct. So, either my intuition (pre-conceived ideas) are wrong, or there is a mistake in there somewhere. Should I keep checking, or should I accept what the maths is telling me?