Projectile Motion Section 3.3

What is a projectile? Projectile Object thrown or launched into the air and is subject to gravity. Parabolic Trajectory

Horizontal and Vertical Components Since a projectile moves in 2-dimensions, it therefore has 2 components just like a resultant vector.

Horizontal Velocity Component NEVER changes - ignore air resistance Initial horizontal velocity equals the final horizontal velocity Gravity DOES NOT work horizontally to increase or decrease the velocity.

Vertical Velocity Component Velocity changes (due to gravity) – free fall Constant acceleration Use constant acceleration equations with viy = 0 m/s

Trajectory Together, the horizontal and vertical components produce what is called a trajectory or path. This path is parabolic in nature.

Projectile Types Horizontal Free Fall Launched at an Angle

Horizontally Launched Projectiles which have NO upward trajectory and NO initial VERTICAL velocity. Vx = constant Viy = 0 m/s

Horizontal Launch Δx = vi Δt + ½ a (Δt )2 Horizontal Vx = constant Δx = vx Δt a = 0 m/s2 Vertical Viy = 0 m/s Δy = ½ g (Δt )2 g = -9.81 m/s2 * Can use these assumptions for all constant acceleration equations

Example 1 A plane traveling with a horizontal velocity of 125 m/s is 525 m above the ground. The pilot decides to drop some supplies to designated target below. How long are the supplies in the air? How far away from point where it was launched will the supplies land?

Example 2 The Leo Frigo Memorial Bridge is 62 m above the Fox River. Suppose you kick a rock horizontally off the bridge. The rock hits the water 12 m from the edge of the bridge. Find the speed at which you kicked the rock.

Free fall assumptions will also apply Launched at an Angle Since the projectile was launched at a angle, the velocity MUST be broken into components!!! Vix = Vi cos θ Viy = Vi sin θ Free fall assumptions will also apply

Derive equation Given just the angle and the distance traveled, find an equation for the height of the object.

Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (a) How long is the ball in the air?

Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (b) How far away does it land?

Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (c) How high does it travel?