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Understanding Projectile Motion at an Angle: Key Concepts and Examples

This guide explores the fundamentals of projectile motion at angles, covering motion in two dimensions with constant velocity on the x-axis and constant acceleration on the y-axis. It discusses initial velocities, parabolic trajectories, and key equations like vxi = v cos(θ) and vyi = v sin(θ). Key points include maximum height, time to reach it, maximum range at 45 degrees, and symmetry in projectile trajectories. Practical examples, including calculations for arrows and cannonballs, illustrate these concepts and enhance understanding of how varying angles affect range and height.

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Understanding Projectile Motion at an Angle: Key Concepts and Examples

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  1. Projectiles at an Angle Physics Mrs. Coyle

  2. Projectiles at an Angle

  3. Projectiles at an Angle http://www.physicsclassroom.com

  4. Projectiles at an Angle • Motion in two dimensions • x-axis constant velocity • y-axis constant acceleration • Parabolic trajectory

  5. Initial Velocity • vxi=vcosq • vyi=vsinq v

  6. A Look at the Velocities

  7. Equations for Projectiles at an Angle • Initial Velocity is at an angle with the horizontal • vx=constant • vy=vyi+at a=-10m/s2 • Dy=vyit+ 1at2 2

  8. Additional Key Points • At the max height: vy=0 vx=constant=vxi • Maximum range when q=45 degrees in the absence of air resistance. • Complementary angles result in the same range. • Symmetry • Resultant velocity is tangent to the curve at the point of study.

  9. Demonstration Link Projectiles at an Angle

  10. Example 1 An arrow is shot with an initial x velocity of 5m/s and an initial y velocity is 15m/s. • How much time will pass for the projectile to reach max height? • What is the max height? • What is the range? Answer: a) t=1.5s , b)y= 11.25m, c) x=15m

  11. Example 2 A cannonball is shot with an initial x velocity of 60m/s and an initial y velocity of 25m/s. a)What is the max height? b)What is the range?Answer: a) t=2.5s, y=31.25m b) x=300m

  12. Example 3 Using vx=vcosq, vy=vsinq A cannonball is shot at 60 degrees with an initial velocity of 40m/s. a)What is the max height? b)What is the range? c)At what angle should the projectile be shot to achieve max range and what is the max range? a)Vx=20m/s, Vy=34.64m/s, t max=3.5s, y=61mb) 140m, c) 45o , 163m

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