3 Projectile Motion Notes (1) - Copy.pdf

Chapter 3 Motion in Two Dimensions 3.3: Projectile Motion projectile An object shot through the air, such as a football, that has independent vertical and horizontal motions and, after receiving an initial thrust, travels through the air only under the force of gravity. trajectory The path of a projectile through space. motion diagram A series of images showing the positions of a moving object taken at regular (equal) time intervals. In today’s lesson you will: • explain how the vertical and horizontal motions of a projectile are related • identify the relationships between a projectile’s height, time in the air, initial velocity, and horizontal distance traveled Main Idea: A projectile’s horizontal motion is independent of its vertical motion. Path of a Projectile • An object shot through the air is called a projectile. • If you ignore air resistance, after an initial force launches a projectile, the only force on it as it moves through the air is gravity. • Gravity causes the object to curve downward. • Its path through space is called trajectory. Independence of Motion in Two Dimensions • The ball on the left was dropped with no initial velocity. The ball on the right was given an initial horizontal velocity. • Because the change in vertical position is the same for both, their average vertical velocities during each interval are also the same. • A projectile launched horizontally has no initial velocity. Therefore, its vertical motion is like that of an object dropped from rest.

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Horizontally Launched Projectiles The horizontal motion of a projectile does not affect its vertical motion The object does not accelerate horizontally because after the initial launch, there are not horizontal forces acting on it. The object’s velocity increases as the force of gravity accelerates it downward. The combination of constant horizontal velocity and uniform vertical acceleration produces a trajectory that has a parabolic shape.

Example : A Sliding Plate You are preparing breakfast and slide a plate on the countertop. Unfortunately, you slide it too fast and it flies off the end of the countertop. If the countertop is 1.05 m above the floor and it leaves the top at 0.75 m/s, how long does it take to fall, and how far from the end of the counter does it land? Step 1: Analyze and Sketch the Problem

Step 2: Solve for the Unknown *Please notice that we’ve chosen the downward direction to be y+. Known:

Step 3: Evaluate the answer • Are the units correct? • Do the signs make sense? • Is the magnitude realistic?

Unknown

Angled Launches • When a projectile is launched at an angle, the initial velocity has a vertical component as well as a horizontal component. • At each point in the vertical direction, the velocity of the object as it is moving upward has the same magnitude as when it is moving downward. Angled Launches and Range • The maximum height is the height of the projectile when the vertical velocity is zero and the projectile has only its horizontal-velocity component. • The range (R) is the horizontal distance the projectile travels when the initial and final heights are the same. Example: The Flight of a Ball A ball is launched at 4.5 m/s at 66” above the horizontal. It starts and lands at the same distance from the ground. What are the maximum height above its launch level and the flight time of the ball? Step One: Analyze and Sketch the Problem

Step Two: Identify the known and Unknown Variables Known:

Unknown:

Step Three: Evaluate the Answer Are the magnitudes realistic?

Forces from Air • The effect of forces due to air has been ignored so far, but air can significantly change the motion of an object. • Air applies a drag force that increases as the relative speed of the air increases. • The air resistance also increases as the surface area of the object that faces the moving air increases. • The strength of the wind and its angle relative to the moving object can affect the motion of a projectile. Main Ideas 1. Velocity Two baseballs are pitched horizontally from the same height but at different speeds. The faster ball crosses home plate within the strike zone, but the slower ball is below the batter’s knees. Why does the faster ball not fall as far as the slower one? 2. Projectile Motion A tennis ball is thrown out a window 28 m above the ground at an initial velocity of 15.0 m/s and 20.0° below the horizontal. How far does the ball move horizontally before it hits the ground? 3.