Introduction to Projectile Motion

Unit 3: Two Dimensional Motion Warm up question: What role does gravity have on an object’s motion?

Real – life projectiles Watch video

Where we’ve been Studied linear motion Motion in one direction Included motion in the x direction (horizontal motion)and y direction (free fall) Where we’re going Combine our understandings of linear motion and vectors to describe and analyze a special kind of two dimensional motion We will use diagrams, numbers, equations, and words for describing and analyzing projectile motion.

Definitions Projectile – An object that is launched by a force and continues to move by its own inertia – it is only under the influence of gravity Trajectory – the path of a projectile. Parabola – geometric shape of the path of a projectile. Range – the total horizontal distance traveled by a projectile

Projectile motion problems are solved by treating horizontal and vertical motion separately. *IMPORTANT* Gravity only affects vertical motion. 1. o oo object launched horizontally 2. o oo object launched at an angle

Objects Launched Horizontally v i = initial horizontal velocity d x = horizontal distance d y = vertical distance(height) t = total time in the air IMPORTANT FACTS There is no horizontal acceleration. There is no initial vertical velocity. The horizontal velocity is constant. Time is the same for both vertical and horizontal. Equation Δd = v i.... t + ½.... a.... t 2 horizontal dx = vi.t vertical dy = 1/2. ag.t2

Object Launched at an Angle v i = initial velocity  = launch angle t = total time in air d x = horizontal range IMPORTANT FACTS The horizontal velocity is constant. The horizontal velocity is constant. Gravity only effects the vertical motion. Gravity only effects the vertical motion. It rises and falls in equal time intervals. It rises and falls in equal time intervals. It reaches maximum height in half the total time. It reaches maximum height in half the total time. When at maximum height, vertical velocity is zero. When at maximum height, vertical velocity is zero. Final vertical velocity is equal to Final vertical velocity is equal to Negative initial vertical velocity Change in vertical position is zero (because it lands at the same height it was launched from) Change in vertical position is zero (because it lands at the same height it was launched from) 

Structure for Problem Solving GUESS has not gone away it just looks a little different. Horizontal (x)Vertical (y) ΔxΔxΔyΔy ViVi ViVi aa tt G: U:

Structure for Problem Solving (Cont.) E: S:Substitute Variables S: Solve

Horizontal Projectile Knowns Horizontal (x)Vertical (y) Δx (given or you will solve for it)Δy (given or you will solve for it) V i (given or you will solve for it)V i = 0 A (constant velocity therefore 0)a = 9.8 m/s 2 t (given or you will solve for it) Note: time will be the same for the horizontal and vertical. Why?

Example 1 A stone is thrown horizontally at 7.5 m/s from a cliff that is 68.4 m high. How far from the base of the cliff does the stone land? Horizontal (x)Vertical (y) ΔxΔxΔyΔy ViVi ViVi aa tt G: U: E:

Example 2 A baseball is thrown horizontally with a velocity of 44 m/s. It travels a horizontal distance of 18 m to the plate before it is caught. a.How long does the ball stay in the air? b.How far does the ball drop during its flight? Horizontal (x)Vertical (y) ΔxΔxΔyΔy ViVi ViVi aa tt G: U: E: