TwoDimensional Motion and Vectors Preview Section 1 Introduction

Two-Dimensional Motion and Vectors Preview Section 1 Introduction to Vectors Section 2 Vector Operations Section 3 Projectile Motion Section 4 Relative Motion Section 1

Two-Dimensional Motion and Vectors Section 3 Projectile Motion • Projectiles: objects that are launched into the air – tennis balls, arrows, baseballs, wrestlers • Gravity affects the motion • Path is parabolic if air resistance is ignored • Path is shortened under the effects of air resistance

Two-Dimensional Motion and Vectors Section 3 Components of Projectile Motion • As the runner launches herself (vi), she is moving in the x and y directions.

Two-Dimensional Motion and Vectors Analysis of Projectile Motion • Horizontal motion – No horizontal acceleration – Horizontal velocity (vx) is constant. • How would the horizontal distance traveled change during successive time intervals of 0. 1 s each? • Horizontal motion of a projectile launched at an angle: Section 3

Two-Dimensional Motion and Vectors Analysis of Projectile Motion • Vertical motion is simple free fall. – Acceleration (ag) is a constant -9. 81 m/s 2. – Vertical velocity changes. • How would the vertical distance traveled change during successive time intervals of 0. 1 seconds each? • Vertical motion of a projectile launched at an angle: Section 3

Two-Dimensional Motion and Vectors Projectile Motion Click below to watch the Visual Concept Section 3

Two-Dimensional Motion and Vectors Projectile Motion - Special Case Initial velocity is horizontal only (vi, y = 0). Section 3

Two-Dimensional Motion and Vectors Section 3 Projectile Motion – Launched at an angle When projectiles are launched at an angle we can use the following equations and use acceleration of gravity. ΔX= Vi (cosθ)Δt Vx = Vi (cosθ) = constant

Two-Dimensional Motion and Vectors Section 3 Projectile Motion Summary • Projectile motion is free fall with an initial horizontal speed. • Vertical and horizontal motion are independent of each other. – Horizontally the velocity is constant. – Vertically the acceleration is constant (-9. 81 m/s 2 ). • Components are used to solve for vertical and horizontal quantities. • Time is the same for both vertical and horizontal motion. • Velocity at the peak is purely horizontal (vy = 0).

Two-Dimensional Motion and Vectors Section 3 Classroom Practice Problem (Horizontal Launch) • A pelican flying along a horizontal path drops a fish from a height of 5. 4 m while traveling 5. 0 m/s. how far does the fish travel horizontally before it hits the water below? • Answer: 5. 0 m

Two-Dimensional Motion and Vectors Section 3 Classroom Practice Problem (Horizontal Launch) • Give both the horizontal and vertical components of the velocity of the fish from the previous problem before the fish enters the water. • Answer: 5. 0 m/s, 9. 8 m/s

Two-Dimensional Motion and Vectors Section 3 Classroom Practice Problem (Horizontal Launch) • A movie director is shooting a scene that involves dropping a stunt dummy out of an airplane and into a swimming pool. The plane is 10. 0 m above the ground, traveling at a velocity of 22. 5 m/s in the positive x direction. The director wants to know where the plane’s path the dummy should be dropped so that it will land in the pool? • Answer: 32. 2 m

Two-Dimensional Motion and Vectors Section 3 Classroom Practice Problem (Horizontal Launch) • Find the instantaneous velocity of the stunt dummy in the previous problem as it hits the water? • Answer: 26. 5 m/s at 31. 913° below the horizontal

Two-Dimensional Motion and Vectors Section 3 Classroom Practice Problem (Horizontal Launch) • A cat chases a mouse across a 1. 0 m high table. The mouse steps out of the way and the cat slides off the table at a speed of 5. 0 m/s. Where does the cat strike the floor? • Answer: 2. 2 m from the table

Two-Dimensional Motion and Vectors Section 3 Classroom Practice Problem (Projectile Launched at an Angle) • In a scene in an action movie, a stuntman jumps from the top of one building to the top of another building 4. 0 m away. After a running start, he leaps at an angle of 15° with respect to the flat roof while traveling at a speed of 5. 0 m/s. Will he make it to the other roof, which is 2. 5 m shorter than the building he jumps from? • Answer: Yes, -2. 3 m

Two-Dimensional Motion and Vectors Section 3 Classroom Practice Problem (Projectile Launched at an Angle) • A golfer can hit a golf ball a horizontal distance of over 300 m on a good day. What maximum height would a 301. 5 m drive reach if it were launched at an angle of 25. 0° to the ground? (At the top of its flight, the ball’s vertical velocity will be zero) • Answer: 70. 3 m

Two-Dimensional Motion and Vectors Section 3 Classroom Practice Problem (Projectile Launched at an Angle) • Salmon often jump waterfalls to reach their breeding grounds. Starting 2. 00 m from a waterfall 0. 55 m in height, at what minimum speed must a salmon jumping at an angle of 32. 0° leave the water to continue upstream? • Answer: 6. 2 m/s

Two-Dimensional Motion and Vectors Section 3 Classroom Practice Problem (Projectile Launched at an Angle) • A quarterback throws the football to a receiver who is 31. 5 m down the field. If the football is thrown at an initial angle of 40. 0 ° to the ground, at what initial speed must the quarterback throw the ball? What is the ball’s highest point during its flight? • Answer: 17. 7 m/s, 6. 60 m