Free Fall

1. Free Fall • Questions / Review • Example 1 – Falling from tower • Example 2 – Thrown downward from tower • Example 3 – Ball thrown upward – symmetric. • Example 4 – Ball thrown upward – asymmetric.

2. Constant acceleration equations a = const v = at + vo x = ½ at2 +vot + xo v2 = vo2 + 2 a x

3. Falling Objects • “Free-fall” means gravity only force. • ALWAYS accelerating down at 9.8 m/s2 • Moment leaves hand – moment hits ground • Sign convention important! • y, v, a, must agree • Usually (+) up, (-) down • If (–) down be consistent • Do positive and negative contributions make sense? • Example 2-10, 2-11 review

4. Falling Objects – 1-way • Example 2-10 – falling from tower • Example 2-11 – falling with vo= 3m/s

5. Falling Objects – 2-way • Example 2-12 / 2-14 – thrown upward vo = +15 m/s • (+) up (-) down! • Initial velocity, position • Velocity, position at 1s. Velocity position 2s • Time to zero velocity. Max height. • Velocity, position at 4s. • Time to hand, velocity. • Symmetry of problem • Time from bottom to top & top to bottom

6. Falling Objects – 2-way • Example 2-12 / 2-14 – thrown upward vo = +15 m/s • Symmetry of problem • Time from bottom to top & top to bottom

7. Falling Objects – 2-way Asymmetric • Example 2-14 thrown 1 m up 15 m/s • Initial velocity, position • y, position • Velocity, position at 1s. Velocity position 2s • Time to zero velocity. Max height. • Max height without time. • Velocity, position at 4s. • Time to ground • Non-physical solution if clocks ran backwards

8. Falling Objects – 2-way Asymmetric • Find when y = 0 • Quadratic Formula • First time a little longer than symmetric case (little greater distance) • Second time as if clock ran backwards (non-physical)