1. How does
the
horizontal
and vertical
motion
differ on
the x- and
y-planes?

3. Horizontally…

4. Vertically…

5. Combined…

6. Combined…

7. Actual…

8. Motion
Diagrams

9. Projectile Motion
For a projectile:
a)
b)
c)
Describe the horizontal and vertical
motion. Horizontal constant velocity
Vertical
accelerating
Describe the horizontal and vertical
Horizontal
zero
acceleration.
Vertical
9.8 m/s2
What equations would you use to
calculate horizontal and vertical
motion. Horizontal v = d/t
Vertical
v = at and d = ½ at2

10. Horizontally…
If you throw a projectile horizontally
Describe the horizontal will it
What is the horizontal
at a speed of 25 m/s, how fast
acceleration for projectile. 3 s?
motion of a a projectile?
be moving, horizontally, after
A projectile moveswill still be
Horizontally, it horizontally
Horizontal acceleration is zero.
with constant25 m/s.
moving at velocity.

11. If a projectile is thrown
What
What a speed
horizontally at
happens, vertically, as a
happens, vertically, as
of 25 m/s, howvertical
Describe the fast is
aprojectile moves
projectile moves
the projectile moving
motion of a projectile.
upward? 3
downward? s?
vertically after
Vertically, a projectile slows
Vertically, a projectile speeds
Vertically, projectile will
a way up.
Vertically,on the projectile
theway down.
down the
up on
accelerates…
be moving 29.4 m/s.
…at a rate of 9.8 m/s2
Vertically…

12. Initially…
25 m/s
0 vertical
velocity
So, if you throw a projectile
horizontally at a speed of After 3 s…
25 m/s
25 m/s, how fast is it
moving after 3 seconds?
actual
30 m/s
Horizontally, it is moving at 25
39 m/s
m/s, vertically it is moving 30
30 m/s
m/s, so (by Pythagorean’s
Theorem) the projectile is moving
25 m/s
at 39 m/s.
motion

13. Group
1
2
3
4
5
6
7
8
9
10
Round 1
Round 2
Round 3

14. B4 stopped
Projectile motion problems…
The key to solving problems involving
projectile motion is…
• understanding that x and y are
independent.
• identifying and separating x and y
variables.
• understanding that time is the same
for both x and y.
• Using appropriate equations for x
and y.

15. Projectile motion problems…
Useful tips…
• Draw a picture.
• Make a table with an x column
and a y column to identify
variables.
• Immediately write down
acceleration due to gravity (g) in
the y column.
• Time connects x and y.

16. Projectile motion problems…
Equations…
• Along the x-axis:
– no acceleration;
moves w/ constant velocity.
– v = d/t
• Along the y-axis:
– Accelerates b/c of gravity; g = 9.8 m/s2.
– v = at
– d = ½at2

17. Lamp on a table…
If I knock a lamp off an end-table with
a horizontal velocity of 5 m/s and
the table is 0.5 meters high, how far
away does the lamp land?
1.6 meters in front of table.

18. B1 stopped
Kickin’ rocks…
A rock is kicked horizontally off a cliff
and lands 125 meters in front of the
cliff. If the cliff is 80 meters high,
how fast is the rock initially kicked?
31.25 m/s horizontally.

19. A2 stopped
Tossing pennies…
A penny is thrown horizontally of a building
with a velocity of 10 m/s. If the penny lands
78 meters in front of the building, how tall is
the building?
It is 304.2 meters tall.

20. Stranded on a mountain…
An airplane traveling at 80 m/s
at an elevation of 250 m, drops
a box of supplies to skiers
stranded in a snowstorm. At
what horizontal distance from
the skiers should the supplies
be dropped?
They need to be dropped 571.43 m
before target (565.69 if using 10).

21. Stranded on a mountain…
(con’t)
What is the speed of the
box as it reaches the
ground?
It is going 106.3 m/s
(106.8 m/s if using 10)

22. Stone throw…
Paco, standing on a
cliff, throws a stone with
a horizontal velocity of
15.0 m/s and the stone
hits the ground 47.0 m
from the base of the cliff.
How high is the cliff?
The cliff is 48 m high.