2. 2015

3. What is projectile motion? Any object that moves through air or space is a form of two-dimensional motion that deals with the motion of objects under the influence of gravity. There is motion in both the horizontal plane (x-axis) and the vertical plane (y-axis).

4. Projectile motion The path in which a projectile travels is a parabolic curve so long as there is no wind resistance. WEEE……

5. Projectile motion problems are best solved by treating horizontal and vertical motion separately. *IMPORTANT* Gravity only affects vertical motion. There are two main types of projectile motion situations. 1. o oo object launched horizontally 2. o oo object launched at an angle

6. Horizontal Motion: If there is no gravity, an object moving horizontally (in the x-direction) would continue to move in a straight line.

7. Vertical Motion If an object is dropped vertically (in the y-direction), the gravity causes it to accelerate downwards.

8. Projectile motion Projectile motion is a combination! In the x- direction, it continues to move at a constant speed, but in the y-direction, it accelerate downward because of gravity!

9. Remember this!!!!!!!!!!! For a projectile: THE X- VELOCITY IS independent of the Y-VELOCITY!!! The speed in the x-direction doesn’t care about what the speed in the y- direction is!

10. Why? Remember that gravity is only pulling in one direction down and nothing is pulling right or left. If there is no gravity, a projectile would go straight forever.

11. Velocity Vectors Remember that velocity has a direction, so it can be represented using vectors! We can break down the velocity into separate x- and y- components.

12. Velocity Vectors Let’s examine the x and y velocity vectors for a projectile: Its x-velocity stays constant and its y- velocity increases.

13. Y-Velocity Just like in freefall: Velocity in the y-direction decreases on the way up, and increases on the way down. At the top of the path, the y-velocity is always zero. Velocity on the way up equals velocity on the way down when you reach the same height.

14. Question #1 If you were walking at a constant velocity with a baseball and threw it up into the air while you were walking, would it fall a. in front of you b. behind you c. right back into your hands

15. Answer Its y-velocity is different than your, but its x- velocity stays the same as you. It should land back in your hands!

16. Question #2 An airplane is carrying a bomb and traveling with a velocity of 1,100 mph east. If it releases its bomb and continues at that velocity, will the bomb land a. directly underneath the plane b. behind the plane c. ahead of the plane

17. Answer If they’re going at the same x-velocity, it will land directly beneath the plane!

18. Projectiles vs. Free Falling Objects Projectiles fall at the same rate as free falling objects.They will hit at the same time, because they are both being pulled by gravity at the same rate! Only one will have a greater x-range.

19. Solving for projectile motion Since projectiles travel in both the horizontal and vertical planes, we can solve for the X and Y components. We can use the one-dimensional motion equations to solve for variables involved in two-dimensional motion problems.

20. Horizontal Projectile Motion School Book Boo….. I don’t like school books!! A VERY TALL BUILDING CRASH!! ! x -y

21. V y = (g)( Δ t) V y ² = 2( g)( Δ y) Δ y = ½(g)( Δ t)² Δ x = (V x,i )( Δ t) Horizontal Projectile Motion Formulas

22. Sample Problem The Royal Bridge in Colarado is 321 m above the Arkansas River. If you kick a rock horizontally off the bridge and it hits the water with a horizontal displacement of 45 m, what is the velocity at which the rock was kicked? Δ y = -321 m g = 9.81 m/s² ΔxΔx Δ x = 45 m Δ y = -½(g)( Δ t)² √-2(Δ y)/g = Δ t 8.1 s = Δ t Δ x = (V x,i )( Δ t) Δ x/ Δ t = V x,i + 5.56 m/s = V x,i