1. Motion in Two Dimensions

2. Projectile Motion A projectile is an object moving in two dimensions under the influence of Earth's gravity; its path is a parabola.

3. Motion in Two Dimensions

4. a y =  g a x = 0 Motion in Two Dimensions

5. Ignoring air resistance, the horizontal component of a projectile's acceleration (A) is zero. (B) remains a non-zero constant. (C) continuously increases. (D) continuously decreases.

6. If an object is launched at an initial angle of θ 0 with the horizontal, the analysis is similar except that the initial velocity has a vertical component.  Motion in Two Dimensions

7. Ignoring air resistance, the horizontal component of a projectile's velocity (A) is zero. (B) remains constant. (C) continuously increases. (D) continuously decreases.

8.  vovo x y Eq 2 Constant acceleration Eq 1 Constant velocity Motion in Two Dimensions

9. A ball is thrown with a velocity of 20 m/s at an angle of 60° above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory? (A) 10 m/s (B) 17 m/s (C) 20 m/s (D) zero

10.  vovo x y Sub Eq 1 Eq 3 Constant velocity Motion in Two Dimensions

11. Practice Problem If V x = 6.80 units and V y =  7.40 units, a) determine the magnitude of V. b) determine the direction of V VxVx V VyVy 

12.  vovo x y Eq 4 Constant acceleration Motion in Two Dimensions

13. A soccer ball is kicked with a velocity of 25 m/s at an angle of 45° above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory? (A) 9.80 m/s 2 downward (B) (9.80 m/s 2 ) × sin (45°) downward (C) (9.80 m/s 2 ) × sin (45°) upward (D) (9.80 m/s 2 ) upward

14. Motion in Two Dimensions When a football in a field goal attempt reaches its maximum height, how does its speed compare to its initial speed? (A) It is zero. (B) It is equal to its initial speed. (C) It is greater than its initial speed. (D) It is less than its initial speed.

15.  vovo h x y Sub into Eq 4 Eq 5 Solve Eq 3 for t Motion in Two Dimensions Vertical Position as a Function of Horizontal Displacement

16.  vovo h x y At the maximum height (v y = 0) Sub into Eq 4 Eq 7 Eq 6 Motion in Two Dimensions Maximum Height

17. Problem A football is kicked at ground level with a speed of 18.0 m/s at an angle of 35.0º to the horizontal. How much later does it hit the ground? Time in the air is twice the time to the top.

18.  vovo R h x y Eq 8 Motion in Two Dimensions Range

19. Motion in Two Dimensions At what angle should a water-gun be aimed in order for the water to land with the greatest horizontal range? (A) 0° (B) 30° (C) 45° (D) 60°

20. The range of a projectile is maximum (if there is no air resistance) for a launch angle of 45°. Motion in Two Dimensions

21. A projectile is fired with an initial speed of 65.2 m/s at an angle of 34.5º above the horizontal on a long flat firing range. Determine (a) the maximum height reached by the projectile. Problem (b) the total time in the air (c) the total horizontal distance covered (that is, the range).

22. You are trying to hit a friend with a water balloon. He is sitting in the window of his dorm room directly across the street. You aim straight at him and shoot. Just when you shoot, he falls out of the window! Does the water balloon hit him? a) yes, it hits b) maybe—it depends on the speed of the shot c) no, it misses d) the shot is impossible e) not really sure Assume that the shot does have enough speed to reach the dorm across the street. Your friend falls under the influence of gravity, just like the water balloon. Thus, they are both undergoing free fall in the y- direction. Since the slingshot was accurately aimed at the right height, the water balloon will fall exactly as your friend does, and it will hit him!! Question 3.10aShoot the Monkey I

23. Shoot the Monkey

24. Eq 1 Horizontal Velocity Eq 2 Vertical Velocity Eq 3 Horizontal Displacement Eq 4 Vertical Displacement Equations

25. Eq 5 Vertical Position Eq 7 Maximum Height Eq 8 RangeEq 6 Time to the Top Equations