Projectiles at an Angle Physics Mr Berman Projectiles

Projectiles at an Angle Physics Mr. Berman

Projectiles at an Angle

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

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

Initial Velocity n vxi=vcosq n vyi=vsinq v

A Look at the Velocities

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

Additional Key Points n n n 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.

Projectiles at an Angle Demonstration Link

Example 1 An arrow is shot with an initial x velocity of 5 m/s and an initial y velocity is 15 m/s. a) How much time will pass for the projectile to reach max height? b) What is the max height? c) What is the range? Answer: a) t=1. 5 s , b)y= 11. 25 m, c) x=15 m

Example 2 A cannonball is shot with an initial x velocity of 60 m/s and an initial y velocity of 25 m/s. a)What is the max height? b)What is the range? Answer: a) t=2. 5 s, y=31. 25 m b) x=300 m

Example 3 Using vx=vcosq, vy=vsinq A cannonball is shot at 60 degrees with an initial velocity of 40 m/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=20 m/s, Vy=34. 64 m/s, t b) 140 m, c) 45 o , 163 m max=3. 5 s, y=61 m