1. Projectile Motion
Introduction
Horizontal launch

2. #1 A ball is dropped from a height of 125 m.
How long does it take the ball to strike the ground?
What is the velocity of the ball at the ground?
#2 A ball rolls at 15 m/s for 5 seconds.
How far does the ball roll?
INCLUDE A LIST OF GIVENS FOR EACH
motion map

3. Projectile motion Projectile – an object with only gravity
acting on it
No air resistance (in our examples)
No propellant
After some initial condition (throwing, etc)

4. Projectile motion vo Which ball hits the ground first?
A: dropped B: launched horizontally vo A B

5. Projectile motion Perpendicular vectors are independent
They do not directly affect each other
Break all 2-D motion into two separate vector components.
Choose easy components that make sense

6. Projectile motion Gravity pulls down (vertical vector),
so it has no effect on the horizontal vector
***This (vertical) should be a dimension
that we analyze
“Horizontal” would then be the other (┴)

7. Projectile motion
Acceleration in the vertical (y) direction will continue to be g = -10 m/s2
ay = m/s2
If air resistance is ignored, there is nothing changing the horizontal velocity*
ax = 0 m/s2 vox = vx
*This may change in future problems

8. Constant acceleration
Projectile motion
Horizontal (x)
Constant velocity
(ax = 0 m/s2)
vox = vx
Equation:
Vertical (y)
Constant acceleration
(ay = -10 m/s2)
Equation:

9. Constant acceleration
Projectile motion
Horizontal (x)
Constant velocity
(ax = 0 m/s2)
vox = vx
Equation:
dx = d0x + vx·t
Vertical (y)
Constant acceleration
(ay = -10 m/s2)
Equation:

10. Constant acceleration
Projectile motion
Horizontal (x)
Constant velocity
(ax = 0 m/s2)
vox = vx
Equation:
dx = d0x + vx·t
Vertical (y)
Constant acceleration
(ay = -10 m/s2)
Equation:
dy = …
vy = …

11. Constant acceleration
Projectile motion
Horizontal (x)
Constant velocity
(ax = 0 m/s2)
vox = vx
Equation:
dx = d0x + vx·t
Determines: ____
Vertical (y)
Constant acceleration
(ay = -10 m/s2)
Equation:
dy = …
vy = …
Determines: ___

12. Constant acceleration
Projectile motion
Horizontal (x)
Constant velocity
(ax = 0 m/s2)
vox = vx
Equation:
dx = d0x + vx·t
Determines: ____
Vertical (y)
Constant acceleration
(ay = -10 m/s2)
Equation:
dy = …
vy = …
Determines time

13. Constant acceleration
Projectile motion
Horizontal (x)
Constant velocity
(ax = 0 m/s2)
vox = vx
Equation:
dx = d0x + vx·t
Determines range
Vertical (y)
Constant acceleration
(ay = -10 m/s2)
Equation:
dy = …
vy = …
Determines time

14. A ball is rolled horizontally off a 125 meter ledge at a speed of 15 m/s.
What is the range of the ball?
(How far will it go horizontally, dx)
What is the velocity when it hits the ground?
magnitude and direction (angle)

15. Projectile Motion
Horizontal launch – v0y = 0 m/s

16. Projectile Motion
Angled launch

17. #1 A ball is thrown upward at 30 m/s from
an 80 meter cliff.
How long does it take the ball to strike the ground?
What is the velocity of the ball at the ground?
#2 A ball rolls at 40 m/s for 8 seconds.
How far does the ball roll?

18. Projectile motion v0 v0 vx v0y
When starting with an angled velocity, show the velocity as a sum of perpendicular components
horizontal (x), and vertical (y) v0 v0 vx
v0y

19. Projectile motion v0 v0y v0y vx vx
Remember, vectors can be moved around v0 vx
v0y vx
v0y

20. A ball is launched off an 80 meter cliff.
The initial velocity of the ball is 50 m/s
at an angle of 37º above horizontal.
What is the range of the ball?
What is the velocity when it hits the ground?

21. Motion Map

22. Motion Map

23. Motion Map

24. Projectile Motion Horizontal launch – v0y = 0 m/s Angled launch
Always find vx and voy first
Never use the total/vector sum in equations
Remember: vy = 0 m/s at max
vx is constant
position has two coordinates
(dx, dy)