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Projectile Motion

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What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

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Yes ExamplesNon Examples Tennis ball Football Golf ball Basketball Javelin Jumping out of a car Cannon ball Plane Rocket Missile

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Projectile Motion Example # 1

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The ball is in free fall vertically and moves at constant speed horizontally!!!

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Conclusions about Projectile motion 1)The horizontal component of a projectile’s velocity is constant (no acceleration) 2)Projectile experiences constant downwards acceleration (gravity) 3)Horizontal and vertical motion of a projectile are independent of each other (except they have a common time)

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Projectile Motion Example # 2

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Important Variables Time – Δt Velocity – v i, v f Height – Δd y Distance – Δd X Acceleration – a Launch Angle - θ

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Strategy to Solving Projectile Motion Problems Analyze horizontal motion and vertical motion independently – Separate the velocity vector into x- and y- components Remember: Time is common between them Use an x/y chart to list givens

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Horizontal motion: - Constant velocity (0 accel.) in the x direction - Equation : v = d/t

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Vertical motion: - Constant acceleration - 9.81 m/s 2 [down] - Use the accel. equations we derived

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Two Types of Problems: One Dimensional Problems (no horiz. Velocity) Case 1: Object dropped from rest Case 2: Object thrown directly upwards Two Dimensional Problems: Case 3: Rolled over an edge Case 4: Shot at an angle

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For Two Dimensional Problems: Break the initial velocity into horizontal and vertical components (using the given angle and trigonometry) v y θ v x

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Projectile Motion Example # 3

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Example Question 1 A tennis ball is rolled off a counter at 8 m/s, what will it’s position be after 3s? Example Question 2 A golfer strikes a golf ball on level ground. The ball leaves the ground with an initial velocity of 42 m/s [32 o above the horizontal]. a) What will the ball’s position be after 4 s? b) What will be the maximum height attained?

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Example # 3: A cannonball is fired with velocity of 50.0 m/s [30º above the horizontal]. It is shot at the level battle field which is located 20.0 m below. a) Calculate the horizontal displacement of the cannonball. b) Calculate the impact velocity of the cannonball

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