1. 1-2-4 Horizontal Projectiles
Over the Edge
Horizontal Projectiles

2. A red ball rolls off the edge of a table
What does its path look like as it falls?
Parabolic path

3. As the red ball rolls off the edge, a green
ball is dropped from rest from the same
height at the same time
Which one will hit the ground first?
They will hit
at the SAME
TIME!!!

4. The same time?!? How?!? The green ball falls from rest
and has no initial
velocity IN EITHER
DIRECTION!
viy and vix = 0
The red ball has an initial
HORIZONTAL velocity (vix)
But does not have any initial
VERTICAL velocity (viy = 0)
vix

5. One Dimension at a Time Both balls begin with no VERTICAL VELOCITY
Both fall the same VERTICAL DISTANCE
This means that the time of flight IS THE SAME IN BOTH CASES

6. Example #1 (not in notes)
A bullet is fired horizontally from a gun that is 1.7 meters above the ground with a velocity of 55 meters per second.
At the same time that the bullet is fired, the shooter drops an identical bullet from the same height.
Prove that the two bullets hit the ground at the same time.
For both bullets…
vi = 0
a = m/s2
d = -1.7 m

7. Need time from vertical
Example #2
An airplane making a supply drop to troops behind enemy lines is flying with a speed of 300 meters per second at an altitude of 3.0 kilometers.
How far from the drop zone should the aircraft drop the supplies?
Need time from vertical
d = vit + ½ at2
3000 m = 0 + ½ (-9.81 m/s2)t2
t = 24.7 s
Use time in horizontal
d = vit + ½ at2
d = (300 m/s)(24.7 s) + 0
d = 7410 m

8. Need time from vertical
Example #3
A stuntman jumps off the edge of a 45 meter tall building to an air mattress that has been placed on the street below at 15 meters from the edge of the building.
What minimum initial velocity does he need in order to make it onto the air mattress?
Need time from vertical
d = vit + ½ at2
45 m = 0 + ½ (-9.81 m/s2)t2
t = 3.03 s
Use time to find v
v = d / t
v = 15 m / 3.03 s
v = 4.95 m /s

9. Example #4
An astronaut on the Moon throws a wrench horizontally with a speed of 0.5 meters per second from a height of 1.5 meters. The astronaut simultaneously drops a feather from the same height. Which object will hit first? Why?
With no air resistance and identical vertical variables they hit the ground at the same time.