Projectiles at an angle
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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

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Projectiles at an angle

Projectiles at an Angle

Physics

Mrs. Coyle


Projectiles at an angle1

Projectiles at an Angle


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


A look at the velocities

A Look at the Velocities


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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