1. Tuesday, 10/8 Turn in lab write up from Friday (late after today) Respond to the following: 1.T or F: The length of the arrow representing a vector should be proportional to the magnitude of the quantity being represented. 2.T or F: When adding vectors, the resultant is always drawn from the point of origin to the point where the last vector ended. Reminders: Linear motion retests need to be completed by Thursday, 10/10 Projectile motion quiz is on Tuesday, 10/15 Unit 3 Tests in on Tuesday, 10/22

3. 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). Range – the total horizontal distance traveled by a projectile

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

5. 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

6. 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) 

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

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

9. 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 VfVf VfVf t (given or you will solve for it) Note: time will be the same for the horizontal and vertical. Why?

10. 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 VfVf VfVf tt G: U: E:

11. 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 VfVf VfVf tt G: U: E:

12. 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 VfVf VfVf tt G: U: E: