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Projectiles at an Angle Physics Mrs. Coyle Projectiles at an Angle Projectiles at an Angle http://www.physicsclassroom.com Projectiles at an Angle Motion in two dimensions x-axis constant velocity y-axis constant acceleration Parabolic trajectory Initial Velocity vxi=vcosq vyi=vsinq v A Look at the Velocities 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 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. Projectiles at an Angle Demonstration Link Example 1 An arrow is shot with an initial x velocity of 5m/s and an initial y velocity is 15m/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=1.5s , b)y= 11.25m, c) x=15m 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 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 b) 140m, c) 45o , 163m max=3.5s, y=61m