1. 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. We can find an object’s displacement in EITHER DIMENSION using TIME
One Dimension at a Time
Both balls begin with no VERTICAL VELOCITY
Both fall the same DISTANCE VERTICALLY
Find time of flight by solving in the appropriate dimension
We can find an object’s displacement in
EITHER DIMENSION using TIME

6. Example #1
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.
Which bullet hits the ground first?
Both hit the ground at the same time

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 300 meters.
How far from the drop zone should the aircraft drop the supplies?
Need time from vertical
dy = viyt + ½ ayt2
300 m = 0 + ½ (-9.81 m/s2)t2
t = 7.82 s
Use time in horizontal
dx = vixt + ½ axt2
dx = (300 m/s)(7.82 s) + 0
dx = 2346 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
dy = viyt + ½ ayt2
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. Need time from vertical
Example #4
A CSI detective investigating an accident scene finds a car that has flown off the edge of a cliff. The car is 79 meters from the edge of the 25 meter high cliff.
What was the car’s initial horizontal velocity as it went off the edge?
Need time from vertical
dy = viyt + ½ ayt2
25 m = 0 + ½ (-9.81 m/s2)t2
t = 2.26 s
Use time in horizontal
dx = vixt + ½ axt2
79 m = vix (2.26 s) + 0
vix = m/s