Chapter 3 Projectile Motion
CONCEPTUAL PHYSICS
HEWITT, 1999
3.1 Vector & Scalar Quantities
 Vector- magnitude and direction (23m/s N)
 Only units that can have direction can be vectors
 Velocity (speedometer & compass)
 Scalar- magnitude only (23m/s, 34°C, 56s, 3L, 85kg)
 Some units simply can’t have direction, like time and
temperature
 Speed (speedometer only)
3.2 Velocity Vectors
 We use an arrow to represent velocity vectors
 Arrow shows direction, length shows relative magnitude
 We can then add, subtract or use other math to find the sum of
all of the vectors
 If drawn correctly, we can just use a ruler!
 Draw to an appropriate scale (1cm=10m/s?)
 Using simple trigonometry (remember a2+b2=c2?),
we can find the sum of non-linear vectors
 PhET “Vector Addition”
Vector Addition
 By placing vectors tail-to-tip, we can line them up to
add them!
Rectangle & Vectors
 A rectangle (or a right triangle) helps us resolve
vectors


Diagonal (or hypotenuse) is the resultant
Parallelogram can be used of the rectangle doesn’t have 90°
angles
 Special Angles
 3,4,5 triangle- angle between 4 & 5 is 37.5°
 1,1,√2 triangle- angle between 1 & √2 is 45°

Gives the maximum range (or distance) when launching/throwing
Example Problem
 If I row my boat north at 80m/s and am caught in a
east cross current of 60m/s, what is my actual
velocity?


802+602 = c2
√(802+602) = 100m/s
 This is a 3,4,5 triangle, so our angle is 37.5°
 Magnitude and direction
 Direction is stated as 37.5° from some reference line (usually
the horizontal or vertical)
 Final answer: 100m/s 37.5° East of North
3.3 Components of Vectors
 Component- a pair of
vectors that can describe
a single vector

Vertical and Horizontal
components
 Resolution- the process of
breaking down a vector
into its components
 CD 3-2 (p9 only)
3.4 Projectile Motion
 Projectiles-Anything that moves vertically (due to earth’s
gravity) and horizontally (independent of g)
 Dimensional independence- Horizontal motion is
independent of gravity
 CD 3-1 (p7-8)
3.5 Upwardly Launched Projectiles
 If the object followed a straight line, then the vertical
distance beneath the line would be the distance that
the ball would have fallen if dropped from that
height



Remember d= ½gt2?
Velocity up is opposite of velocity down at the same elevation
Always ignoring air resistance
Would slow down the projectile
 Figure 3.15

Projectile Resolution
Projectile Resolution
 Look at the horizontal components. Do they ever change?
What does that tell you?
 Look at the vertical velocity components for the same height.
They should be the same, just in opposite directions. What
does this say about velocity?
 These paths ignore air resistance. What would the path
actually look like if air resistance was added? Would the
object go farther/higher or shorter/lower?
 CD 3-2 (p10 only)
 Physlet I3.4, E3.5, P3.8
3.6 Fast-Moving Projectiles- Satellites
 Satellite- an object that is really falling toward the
earth as fast as the earth is moving away from it




If you throw a ping-pong ball, it won’t go very far.
If you throw a baseball very fast; it will travel very far.
What about shooting a bullet? It travels even farther.
“Falls” above the atmosphere to avoid air resistance
 A rocket can “throw” itself fast enough to travel to
the end of the earth, but then the earth has moved,
so it keeps falling…
Satellite Motion
Homework & Assessments
 Review Questions 1-18
 Plug & Chug 1-10
 Think & Explain 1-4
 Chapter 2-3 Exam