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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

Physics

Mrs. Coyle

### 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

• vxi=vcosq

• vyi=vsinq

v

### 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

• 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

### 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

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 max=3.5s, y=61mb) 140m, c) 45o , 163m