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Understanding the Initial Velocity of Angled Projectile Motion

This guide explores the calculations involved in determining the initial velocity components of a projectile launched at an angle. It covers the decomposition of initial velocity into horizontal (vix) and vertical (viy) components using trigonometric functions. The guide provides step-by-step examples, including the case of a soccer ball kicked at an angle, detailing how to calculate maximum height, time to reach maximum height, and horizontal distance traveled. Key assumptions about projectile motion are also discussed for a comprehensive understanding.

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Understanding the Initial Velocity of Angled Projectile Motion

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  1. Fire Away!!! Ground Launched Projectiles

  2. Initial Velocity of an Angled Projectile • Problems will usually only give you the INITIAL VELOCITY and an ANGLE • You must break up the initial velocity into its X and Y COMPONENTS before you can solve the problem • vix= vicosθ • viy= vi sin θ

  3. Initial Velocity Example Calculate the horizontal part of the soccer ball’s initial velocity Calculate the vertical part of the soccer ball’s initial velocity vix = vicosθ viy = vi sin θ 12 m/s 6 m/s 30° 10.4 m/s

  4. Vertical Axis • Which assumptions can we make? • Initial velocity (viy= vi sin θ) • Acceleration due to gravity = -9.81 m/s2 • At max height vfy= 0m/s • Time to max height = ½ total flight time • When the projectile lands, vfy = -viy

  5. Horizontal Axis • Which assumptions can we make? • Initial velocity (vix= vicosθ) • acceleration = 0m/s2 • Horizontal velocity is CONSTANT! • Maximum Range = vix× total flight time

  6. Projectile Vector Diagram vy at top = 0 Parabolic Path ax = 0 ay = -9.81 m/s2 vfy = -viy

  7. Example • The soccer ball from the previous problem is now kicked with an initial velocity of 15m/s at an angle of 37°. • (a) Determine the horizontal and vertical components of the initial velocity • (b) Calculate the maximum height the ball reaches • (c) Calculate the time it takes to reach max height • (d) Find how far the ball lands from the player

  8. (a) Determine the horizontal and vertical components of the initial velocity • (b) Calculate the maximum height the ball reaches

  9. (c) Calculate the time it takes to reach max height • (d) Find how far the ball lands from the player

  10. SUMMARY • How would you calculate the vertical component of the initial velocity? • How would you calculate the horizontal component of initial velocity? • List all of the Vertical axis assumptions • List all of the Horizontal axis assumptions

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