1. Vectors & Projectile Motion Chapter 3

2. Horizontal & Vertical Motion

3. Things to remember for 2D motion Vertical and horizontal motion are independent. When something is traveling through the air, ignore the effects of air resistance. There is nothing pushing or pulling a projectile horizontally, therefore a x =0. For vertical motion, gravity is causing the vertical acceleration, so a y =-9.8m/s 2. We will assume that projectiles landing at a height different from their initial height are always launched horizontally. Therefore, any initial velocity is an x piece. There is no y component for initial velocity.

4. Horizontal Components a=0

5. Vertical Components V iy =0 a=g

6. Example #7 – A Cliff Problem A car drives off a 100m cliff at a speed of 47m/s. What is: –The time it takes to hit the ground? –It’s horizontal distance from the base of the cliff? –It’s final velocity?

7. Identify Vertical and Horizontal Components Horizontal v i =47m/s v f =47m/s a=0 t=? x=? Vertical a=g=-9.8m/s 2 v i =0 y=100m t=? v f =?

8. Part A Use y pieces because there is not enough information to solve for t using x components. Since the car stops moving horizontally at the same time it stops moving vertically, the t found using the y components can be used for the x components as well.

9. Part B

10. Part C The car is going both down and over at the end so v f has both x and y components. v fx = v ix v fy must be calculated.

11. Part C Continued Put x and y components together and solve for both resultant and angle. c v fx v fy 

12. Example #8 A ball is launched horizontally at 10 m/sec off of a 1.2 m tall table. Calculate the following: A)The time in the air. B)How far from the table does the ball land? C)What is the velocity of the ball just before it hits the ground?

13. Example #9 A ball is launched off of a table. If it lands 3.4 m away from 0.85 m tall table, A)How long is it in the air? B)What is the launch velocity? C)What is the final velocity of the ball?

14. Projectile Motion in Football

16. Starting and Ending at the Same Height

17. Example #10 A cannon ball gets fired at a 30 degree angle at 26 m/sec. A)How far away does it land? B)How long is it in the air? C)What is the maximum height? D)How fast is it moving when it hits the ground? E)How fast is the ball moving and how high is the ball 0.6 sec after launch?

18. Example #11 A) How fast is it hit? B) What is the velocity just before the ball hits the ground? C) How high did it go? D) Some lady next to him hit the ball with the same velocity but instead the ball went very high. Her ball landed at the same place. At what angle did she hit the ball? A golf ball is driven at a driving range and lands 100 m away from the golfer. If it is hit at a 15 degree angle,

21. Monkey Hunter!