1. Accurate Measurements

2. Aristotle 384 – 322 BC Foremost scientist of ancient Greeks “Natural for a horse to be horse like.” Natural for light things to rise – like a puff of smoke Heavy things – to fall The heavier the faster He never...

3. The Protractor Tycho Brahe 1546 –1601 Accuracy to one minute of arc 1/60 degree = 1 nautical mile sextant

4. Galileo Galileo Galilei 1564 –1642 Aristotle - “Heavier things fall faster” “All objects fall with the same constant acceleration.”

5. Acceleration Acceleration – How quickly the velocity changes a = dv / dt Velocity – How quickly the position changes v = dx / dt When things fall acceleration = a = 9.8 m/sec/sec ≈ 10 m/s 2

6. Falling Objects a = 9.8 m/sec/sec = g dv/dt = g ∫ dv = ∫ g dt v − v 0 = g(t − t 0 ) v = v 0 + g t dx/dt = v 0 + g t ∫ dx = ∫ (v 0 + g t) dt x − x 0 = v 0 t + ½ g t²

7. Without Calculus ∆ v = g ∆t change in v ∝ time v 2 − v 1 = g (t 2 − t 1 ) Δv ~ t v 2 = v 1 + gt v avg = v̄ = ½ (v 1 + v 2 ) distance = s = ∆x = x 2 − x 1 = v̄ t s = ½ (v 1 + v 2 ) t = ½ (v 1 + v 1 + gt) t s = v 1 t + ½ gt 2