2. Projectile motion is a form of two- dimensional motion in which a “projectile” is under the influence of gravity. Projectile motion is a form of two- dimensional motion in which a “projectile” is under the influence of gravity. There is motion in both the horizontal plane (x-axis) and the vertical plane (y-axis). What is projectile motion?

3. What is a projectile? Projectiles are objects that are launched into the air. Projectiles are objects that are launched into the air. Ex. balls, arrows, long jumpers Ex. balls, arrows, long jumpers

4. Projectile motion The path in which a projectile travels is a parabolic curve (assuming there is no wind resistance). The path in which a projectile travels is a parabolic curve (assuming there is no wind resistance).

5. Projectiles vs. Free Falling Objects Projectiles fall at the same rate as free falling objects.

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

7. Projectile Motion x-Motion y-motion x-Motion y-motion V avg =Δx/Δt Δy = ½ (v i + v f ) Δt V avg =Δx/Δt Δy = ½ (v i + v f ) Δt g = (v f - v i ) / Δt g = (v f - v i ) / Δt Δy = v i Δt + ½ gΔt² Δy = v i Δt + ½ gΔt² v f ² = v i ² + 2gΔy v f ² = v i ² + 2gΔy The same equations we used in 1-D motion! The trick is to solve for “x” and “y” motion of 2-D moving objects independently!

8. Projectile Motion Two types of projectile motion situations: Two types of projectile motion situations: 1. Horizontally launched projectiles 1. Horizontally launched projectiles 2. Projectiles launched at an angle 2. Projectiles launched at an angle

9. Horizontal Projectile Motion Physics Book What am I going to do about book checks??? A VERY TALL BUILDING CRASH !!! x -y

10. 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 = 45.0 m Δ y = ½(g)( Δ t)² √2(Δ y)/g = Δ t 8.10 s = Δ t Δ x = (V x,i )( Δ t) Δ x/ Δ t = V x,i 5.56 m/s = V x,i