CONCEPTUAL PHYSICS HEWITT, 1999 Chapter 3 Projectile Motion.
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Transcript of CONCEPTUAL PHYSICS HEWITT, 1999 Chapter 3 Projectile Motion.
CONCEPTUAL PHYSICSHEWITT, 1999
Chapter 3 Projectile Motion
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) 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
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
componentsResolution- the
process of breaking down a vector into its components
3.4 Projectile Motion
Projectiles-Anything that moves vertically and horizontally due to earth’s gravity
Dimensional independence- Horizontal motion is independent of gravity
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
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?
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