2. 3-3 Projectile Motion Two Dimensional Motion of Objects  Projectile Motion – If air resistance is disregarded, projectiles follow parabolic trajectories.  Projectile - any object that the only force is gravity.  Projectile Motion – free-fall with an initial horizontal velocity. Baseball Projectile Motion

3. Horizontal and Vertical components – independent of each other - both land at same time.

4.  Assuming no air resistance - Horizontal Velocity (Vx) remains constant during entire path. The ball moves the same horizontal distance in equal time intervals.  Velocity in the vertical direction (Vy) – changes by 9.8 m/s every second.

5. X and Y components of a velocity vector can simplify projectile motion.

6. Observe Velocity Vectors: Vertical component changes (by -9.8 m/s every second) while Velocity in X direction remains constant

7. EQUATIONS ∆x = v x tv x = ∆x t Horizontal Launch Up and Down ∆y = ½ g t 2 ∆y = ½ g ( t / 2 ) 2 v y = g t v y = g ( t / 2 ) where t = total time t= √2 ∆y / g t = Square root of 2 times the vertical distance divided by g

8. Projectiles Launched At An Angle Resolve the initial velocity into x and y components. The initial vertical velocity is the y component. The initial horizontal velocity is the x component. V x = V x,i = v i cos θ = constant V y = V i sin θ Use Pythagorean theorem and inverse Tangent function to find resultant and angle. (V i )

9. Suppose a rescue airplane drops a relief package while it is moving with a constant horizontal speed at an elevated height. Assuming that air resistance is negligible, where will the relief package land relative to the plane? a. below the plane and behind it. b. directly below the plane c. below the plane and ahead of it

10. Suppose a rescue airplane drops a relief package while it is moving with a constant horizontal speed at an elevated height. Assuming that air resistance is negligible, where will the relief package land relative to the plane? a. below the plane and behind it. b. directly below the plane c. below the plane and ahead of it

11. If the monkey lets go of the tree the moment that the banana is fired, then where should she aim the banana cannon? a) Below the Monkey b) Above the monkey c) At the monkey

12. If the monkey lets go of the tree the moment that the banana is fired, then where should she aim the banana cannon? a)Below the Monkey b)Above the monkey c)At the monkey