Introduction to basic physic concepts and practical applications of projectile motion.

1. Projectile Motion

2. Background
• An object launched into space without motive
power of its own is called a projectile. Neglect
air resistance, and only gravity causes a
projectile to deviate from a straight line.
• Without motive power, the projectile has a
constant horizontal velocity.
• Under these conditions, the motion of a
projectile can be calculated in 2 dimensions.

3. Horizontal Projection + Free Fall
Note vertical
velocity and
position increase
with time as a free-falling
body.
Horizontal distance
increases linearly
with time, indicating
a constant
horizontal velocity.

4. Projectile Motion at an Angle
Note:
• Vertical velocity (Vy) = 0 at Ymax
• Ө = angle of projection
• Vyo = Vo sin (Ө)
• Vxo = Vo cos (Ө)

5. Objectives
Following this exercise, you should:
• know how to treat motion with constant velocity in
two dimensions.
• know how to treat motion with constant acceleration
in two dimensions.
• be able to apply the equations for two-dimensional
motion to a projectile.
• be able to calculate positions, velocities, and times for
various types of projectile motion.

6. Projectile Motion Equations
Topic Equation Explanation
constant velocity X = X0 + V0xt
Each direction obeys the constant Y = Y velocity equation independently. 0 + Y0xt
constant acceleration: horizontal component
V= V+ at
x ox xV2 = Vx
ox
2+2ax(X-X0)
X = X0 + 1/2(Vox + Vx)t
X = X0 + Voxt + 1/2axt2
constant acceleration: vertical component
V= V+ at
y oy yV2 = Vy
oy
2+2ay(Y-Y0)
Y = Y0 + 1/2(Voy + Vy)t
Y = Y0 + Voyt + 1/2ayt2
range of a projectile S = (2Vo2/ay)sin 2ᶿ
Horizontal distance (S) traveled if the initial height (Yo) equals the final height
(Y).ᶿ equals the angle between the initial projectile direction and horizontal.
flight time of projectile t = (2Vo/ay)sin 2ᶿ
Total time in the air if the initial height equals the final height. ᶿ equals the
angle between the initial projectile direction and horizontal.

7. Questions
• Do we have to know the mass of the object?
– NO. Gravity acts on large and small objects
equally.

8. Questions
• Do we have to know either the distance
traveled, time traveled or the velocity of the
projectile to calculate other parameters?
– YES. The only constant available is gravity
(g or –ay).

9. Example – Horizontal Projection
Vo = ?
Ymax = 100 cm
Xmax = 500 cm

10. Example – Horizontal Projection
• Known:
– Vyo = 0
– g = -ay = 9.81 m/sec
– Ymax = 100 cm = 1 m
– Xmax = 500 cm = 5 m

11. Example – Horizontal Projection
• Key point: velocity = distance/time
– Horizontal distance is known (5 m)
– Horizontal travel time = “free fall” time
– Y = Voy t + ½ a t2
– Initial vertical velocity (Voy) = 0

12. Example – Horizontal Projection
• Calculation
– Y = 1 m = ½ 9.81 m/sec2 t2
– t = [1 m (2)/9.8 m/sec2]1/2 = 0.45 sec
– Vox = Xmax/t = 5 m/0.45 sec
– Vox = 11.1 m/sec

13. Practical Application
In 1957, Homer (Sony) Hickam and 5 other
teenagers in Coalwood, West Virginia were
designing and building miniature rockets. The
boys were accused by authorities of starting a
forest fire as a result of an errant rocket launch.
The boys were suspended from school until
Homer was able to make his case to the Principal
of the High School using his understanding of
projectile motion…
http://movieclips.com/u6Kx-october-sky-movie-homer-proves-his-innocence/#.
TqsNdRK2N0U.email