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 (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

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 (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)

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
0=𝑦= 1 2 (−9.8 𝑚 𝑠 2 ) 𝑡 𝑚 𝑠 𝑡+1𝑚
Quadratic Formula
𝑡= −15 ± −4∙(−4.9)(1) 2∙(−4.9)
𝑡= −15 ± −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)

9. Other examples
Problem 41
Problem 46
Problem 49