What is Projectile Motion?

Projectile Motion A projectile is an object moving in two dimensions under the influence of Earth's gravity Two-dimensional motion of an object Vertical Horizontal

Types of Projectile Motion Horizontal Motion of a ball rolling freely along a level surface Horizontal velocity is ALWAYS constant Vertical Motion of a freely falling object Force due to gravity Vertical component of velocity changes with time Parabolic Path traced by an object accelerating vertically while moving horizontal

3-7 Projectile Motion It can be understood by studying the horizontal and vertical motions separately. Are the same velocity vector Path of object Figure 3-20. Caption: Projectile motion of a small ball projected horizontally. The dashed black line represents the path of the object. The velocity vector at each point is in the direction of motion and thus is tangent to the path. The velocity vectors are green arrows, and velocity components are dashed. (A vertically falling object starting at the same point is shown at the left for comparison; vy is the same for the falling object and the projectile.) velocity components 4

Examples of Projectile Motion Launching a Cannon ball The speed in the x-direction is constant; in the y-direction the object moves with constant acceleration (g) because of gravity.

THE COMPONENTS Vertical Question: Velocity decreases on the way up and increases on the way down (free fall) And at the top of its path, velocity is what? Acceleration is the same up and down when you reach the same height Question: If you were walking at a constant velocity with a baseball and threw it up in the air while you were walking, would it fall In front of you Behind you Right back in your hands

Solving Problems Involving Projectile Motion Example: Where does the apple land? A child sits upright in a wagon which is moving to the right at constant speed as shown. The child extends her hand and throws an apple straight upward (from her own point of view), while the wagon continues to travel forward at constant speed. If air resistance is neglected, will the apple land behind the wagon in the wagon in front of the wagon? Figure 3-25. Response: The child throws the apple straight up from her own reference frame with initial velocity vy0 (Fig. 3–25a). But when viewed by someone on the ground, the apple also has an initial horizontal component of velocity equal to the speed of the wagon, vx0. Thus, to a person on the ground, the apple will follow the path of a projectile as shown in Fig. 3–25b. The apple experiences no horizontal acceleration, so vx0 will stay constant and equal to the speed of the wagon. As the apple follows its arc, the wagon will be directly under the apple at all times because they have the same horizontal velocity. When the apple comes down, it will drop right into the outstretched hand of the child. The answer is (b). 8

TAKE HOME MESSAGE The X-velocity is independent of the Y- velocity The speed in the x-direction (horizontal) doesn’t care what the speed in the y- direction (vertical) is! WHY?

REVIEW QUESTION Suppose two balls are released from the same height: One is dropped from rest the other is thrown horizontally. Which will hit the ground first? Why?

Factors Affecting Projectile Motion What two factors would affect projectile motion? Angle Initial velocity (height – y dist) (range – x dist) Initial Velocity Angle

THE FACTORS Angle Initial velocity 0°- 45° = range increases 45° - 90° = range decreases Initial velocity Greater initial velocity= farther it will go The faster it goes horizontally, more ground is covered

vxi, vx = Horizontal velocity of a projectile HORIZONTAL EQUATIONS SYMBOLS dx= Horizontal displacement (RANGE) vxi, vx = Horizontal velocity of a projectile

dy= vertical displacement (HEIGHT) VERTICAL EQUATIONS SYMBOLS Symbols dy= vertical displacement (HEIGHT) g = acceleration of gravity (9.81 m/s²) Vyi = initial vertical velocity (m/s) Vyf = final vertical velocity (m/s) Vy = vertical velocity

Object Launched Horizontally vx = initial horizontal velocity dy = initial height above ground t = total time in the air dx = horizontal range 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.