2. Two objects are launched off a table top as shown in the diagram and land in the indicated positions.
Which object had the larger initial velocity?
A) Object A
B) Object B
C) They had the same initial velocity
D) It is not possible to tell without more information

3. Two objects are launched off a table top as shown in the diagram and land in the indicated positions.
Which object was in the air longer?
A) Object A
B) Object B
C) They were in the air for the same amount of time
D) It is not possible to tell without more information

4. General Launch Angle Equations of Motion

5. General Launch Angle Equations of Motion

6. General Launch Angle Equations of Motion

7. General Launch Angle Equations of Motion
Putting the origin at the launch point…
(The book does it this way now!)

8. General Launch Angle Equations of Motion

9. Chipping from the rough, a golfer sends the ball over a 3
Chipping from the rough, a golfer sends the ball over a 3.00-m-high tree that is 14.0 m away. The ball lands at the same level from which it was struck after traveling a horizontal distance of 17.8 m. The ball leaves the club at 54.0º above the horizontal and lands on the green 2.24 s later.
What was the initial speed of the ball?

10. Chipping from the rough, a golfer sends the ball over a 3
Chipping from the rough, a golfer sends the ball over a 3.00-m-high tree that is 14.0 m away. The ball lands at the same level from which it was struck after traveling a horizontal distance of 17.8 m. The ball leaves the club at 54.0º above the horizontal and lands on the green 2.24 s later.
What was the initial speed of the ball?
How high was the ball when it passed directly over the tree?

11. A cannon sits at the top of a 135 m tall cliff
A cannon sits at the top of a 135 m tall cliff. It fires a cannonball with initial velocity 235 m/s at an initial angle of 37.0º above the horizontal.
(a) How long is the cannonball in the air?

12. A cannon sits at the top of a 135 m tall cliff
A cannon sits at the top of a 135 m tall cliff. It fires a cannonball with initial velocity 235 m/s at an initial angle of 37.0º above the horizontal.
(a) How long is the cannonball in the air?
(b) How far from the base of the cliff does the cannonball land?

13. “Range”
Range Equation:
What is x when y = 0?

14. “Range”
Range Equation:

15. For a given initial speed, what angle will make the projectile go furthest?
B) 30º
C) 45º
D) 60º
E) 75º

16. The range equation is maximized when q = 45º
WHY???
The range equation is maximized when q = 45º