Projectiles at an Angle

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