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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. v xi =vcos q

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projectiles at an angle

Projectiles at an Angle

Physics

Mrs. Coyle

projectiles at an angle2
Projectiles at an Angle

http://www.physicsclassroom.com

projectiles at an angle3
Projectiles at an Angle
  • Motion in two dimensions
  • x-axis constant velocity
  • y-axis constant acceleration
  • Parabolic trajectory
initial velocity
Initial Velocity
  • vxi=vcosq
  • vyi=vsinq

v

equations for projectiles at an angle
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
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.
demonstration link
Demonstration Link

Projectiles at an Angle

example 1
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

example 2
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 v x vcos q v y vsin q
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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