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.

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

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

Falling Objects – 1-way (down positive) Example 2-10 – falling from tower Example 2-11 – falling with vo = 3m/s time accel velocity distance 0+ s 9.8 m/s2 0 m/s 0 m 1 s 9.8 m/s 4.9 m 2 s 19.6 m/s 19.6 m 3 s 29.4 m/s 44.1 m time accel velocity distance 0+ s 9.8 m/s2 3 m/s 0 m 1 s 12.8 m/s 7.9 m 2 s 22.6 m/s 25.6 m 3 s 32.4 m/s 53.1 m

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

Falling Objects – 2-way (down negative) Example 2-12 / 2-14 – thrown upward vo = +15 m/s Symmetry of problem Time from bottom to top & top to bottom time accel velocity distance 0 s -9.8 m/s2 +15 m/s 0 m 1 s + 5.2 m/s 10.1 m 1.53 s 0 m/s 11.48 m 2 s - 4.6 m/s 10.4 m 3.06 s - 15 m/s 4 s -24.2 m/s -18.4 m (off scale)

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

Falling Objects – 2-way Asymmetric Find when y = 0 0=𝑦= 1 2 (−9.8 𝑚 𝑠 2 ) 𝑡 2 + 15 𝑚 𝑠 𝑡+1𝑚 Quadratic Formula 𝑡= −15 ± 15 2 −4∙(−4.9)(1) 2∙(−4.9) 𝑡= −15 ± 225+19.6 −9.8 𝑡= −15 ±15.64 −9.8 =3.12 𝑠 𝑜𝑟 −.065 𝑠 First time a little longer than symmetric case (little greater distance) Second time as if clock ran backwards (non-physical)

Other examples Problem 41 Problem 46 Problem 49