1. 2 DIMENSIONAL KINEMATICS
MIT C.P. PHYSICS
2 DIMENSIONAL KINEMATICS

7. Zero Angle Projectile Motion

8. Zero Angle Projectile Motion

9. Zero Angle Projectile Motion

10. Zero Angle Projectile Motion

11. Zero Angle Projectile Motion

12. Zero Angle Projectile Motion
Which Ball Will Hit The Ground First?

13. Zero Angle Projectile Motion
Neither!!!!

14. Lab: Zero Angle Trajectory
Interactive

15. Lab: Zero Angle Trajectory
Data Chart 1
Trial #
Height (m)
Angle (°)
Speed (m/s)
Range (m)
Time (s) 1 25 15 2 50 3 75 4
100

16. Lab: Zero Angle Trajectory
Data Chart 2
Trial #
Height (m)
Angle (°)
Speed (m/s)
Range (m)
Time (s) 1
100 30 2 40 3 50 4 60

17. Formulas Time Range Height Velocity h = 1/2gt^2 v = d/t t = √2h/g
d = vt
v = gt
t = d/v

18. Sample Problem 1
A student rolls a ball with a velocity of 35 m/s off a flat table 1.6 m above the floor.
How long does it take to hit the ground?
How far does the ball land away from the table?
t = √2h/g
Step 1
t = √2(1.6)/9.81
Step 2
t = 0.57 s
Step 3

19. Sample Problem 1
A student rolls a ball with a velocity of 35 m/s off a flat table 1.6 m above the floor.
How long does it take to hit the ground?
How far does the ball land away from the table?
Step 1
d = vt
Step 2
d = (35)(0.57)
Step 3
d = 20. m

20. How long does it take to hit the ground? How high is the building?
Sample Problem 2
A student rolls a ball with a velocity of 20.0 m/s off a roof. It lands 82.0 m away from the building.
How long does it take to hit the ground?
How high is the building?
t = d/v
Step 1
t = 82/20.0
Step 2
t = 4.10 s
Step 3

21. How long does it take to hit the ground? How high is the building?
Sample Problem 2
A student rolls a ball with a velocity of 20.0 m/s off a roof. It lands 82.0 m away from the building.
How long does it take to hit the ground?
How high is the building?
Step 1
h = ½ gt^2
Step 2
h = ½(9.81)(4.10)^2
Step 3
h = 82.5 m

22. Problem
Two cannons, each at a different height, aim directly at each other. What will happen if both cannons fire at the same time at each other?

23. Answer

24. Launch Angle Trajectory

25. Launch Angle Trajectory Demo

26. Velocity & Launch Angle
Range & Time & Height
Velocity & Launch Angle

27. Lab: Validating Projectile Formulas
Interactive

28. Lab: Validating Projectile Formulas
Data Chart 1
Trial #
Velocity (m/s)
Angle (°)
Height (m)
Range (m) 1 6 70 2 10 3 14 4 18 5 21

29. Lab: Validating Projectile Formulas
Data Chart 2
Trial #
Velocity (m/s)
Angle (°)
Height (m)
Range (m) 1 15 10 2 20 3 30 4 40 5 50 6 60 7 70 8 80

30. Formulas
Range
d = v^2 sin2Θ/g

31. Which launch angle (30°,45°,60°)will give you the maximum range?
Sample Range Problem
Which launch angle (30°,45°,60°)will give you the maximum range?
Step 1:
d = v^2 sin2Θ/g
Step 2:
d = 1^2 sin2(30°) (9.81)
d = 1^2 sin2(45°) (9.81)
d = 1^2 sin2(60°) (9.81)

32. Which launch angle (30°,45°,60°)will give you the maximum range?
Sample Range Problem
Which launch angle (30°,45°,60°)will give you the maximum range?
0.107 m
0.159 m
0.107 m
Home Run

33. Formulas
Range
Height
d = v^2 sin2Θ/g
h = v^2 sinΘ/2g

34. Sample Height Problem
A ball is kicked up into the air at 35.0°. Its initial velocity was 25.0m/s. How high will the ball travel?
Step 1:
h = v^2(sinΘ)/2g
Step 2:
h = (25.0)^2(sin35.0°) 2(9.81)
Step 3:
18.2m

35. Formulas Range Height Time d = v^2 sin2Θ/g h = v^2 sinΘ/2g
T = 2v sinΘ/g

36. Lab: Determine the Velocity of a Marble Launcher

37. Lab: Determine the Velocity of a Marble Launcher
Data Chart
Trial #
Angle (°)
Distance (m) 1 2 3 4 5

38. Formulas Velocity Velocity Velocity v = √dg/sin2Θ v = √h2(g)/sinΘ
v = Tg/sin2Θ

39. Sample Velocity Problem
A ball is kicked up into the air at 35.0°. It lands 8.01 meters away. What was its initial velocity?
Step 1:
v = √dg/sin2Θ
Step 2:
v = √(8.01)(9.81) sin2(35°)
Step 3:
9.14 m/s

40. Lab: Delude Challenge

42. Test Review Game Added Points Score(Single) Score(Double) 1 3000 15002
3500
1750 3
4000
2000 4
4500
2250 5
5000
2500 6
5500
2750 7
6000 8
6500
3250 9
7000 10
7500
3750

43. Lab: Determine the Velocity of a Potato Launcher