Projectiles at an Angle
Physics
Mrs. Coyle
Projectiles at an Angle
Projectiles at an Angle
http://www.physicsclassroom.com
Projectiles at an Angle
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Motion in two dimensions
x-axis constant velocity
y-axis constant acceleration
Parabolic trajectory
Initial Velocity
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vxi=vcosq
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vyi=vsinq
v
A Look at the Velocities
Equations for Projectiles at an
Angle
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Initial Velocity is at an angle with the
horizontal
vx=constant
vy=vyi+at
a=-10m/s2
Dy=vyit+ 1at2
2
Additional Key Points
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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