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Chapter 3 Projectile Motion Notes

Introduction

- Nonlinear Motion- Motion along a curved path.

e.g. throwing a baseball, cannon, ball rolling

off table. - 2 independent components of motion
- Horizontal remains constant w/o a force acting

on it. - Vertical changes w/ time, g pulls object ? at

10m/s/s. - ? Combined effects produce a curved path,

however, neither component affects the other. - Vectors (arrows) help us understand this motion.

3.1 Vector and Scalar Quantities

- Vector quantity A quantity that requires both

magnitude direction. - e.g. velocity, acceleration
- Scalar quantity A quantity that is described by

magnitude only. Can be added, subtracted,

multiplied divided. - e.g. mass, volume time
- Arrows are used to represent vector quantities.
- length of arrow magnitude
- direction of arrow direction of vector

quantity

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3.2 Velocity Vectors

- Follow on the Board
- Suppose an airplane is flying north at 100km/h

and there is a tailwind blowing north at a

velocity of 20km/h. - Suppose the same airplane turns around and flies

into the wind. - Suppose an airplane flying north at 80km/h caught

a strong crosswind of 60km/h blowing west to east.

3.2 Continued

- Resultant the result of adding two vectors.
- How do you find the resultant?
- Vectors at right angles
- Draw 2 vectors with tails touching
- Draw parallel projection of each vector with

dashed lines - Draw the diagonal (from point where tails are

touching) - Vectors not at right angles
- Form a parallelogram, the resultant is its

diagonal. - Note To add 2 vectors that are equal in

magnitude at right angles, we use a square.

The diagonal is the square root of 2 or 1.414

times the length of one of its sides.

3.3 Components of Vectors

- Any vector can be broken down into its vertical

and horizontal vectors, called components. - Resolution process of determining the components

of a vector. (p. 32, Figure 3.7) - Vertical and Horizontal lines are drawn from the

tail of the vector. - A rectangle is drawn that encloses the vector as

its diagonal. - Sides of the rectangle are the desired components.

3.4 Projectile Motion

- Projectiles stone thrown in air, cannon ball,

etc. - Projectile Motion
- ?Horizontal velocity remains constant when no

horizontal force acts on projectile. - ? Vertical velocity changes dues to gravity.
- Combined affect produces curved path, parabola.

3.5 Upwardly Launched Projectiles

- No gravity projectile follows straight-line

path. - With gravity projectile falls beneath line,

same vertical distance it would fall from rest. - d ½ gt2 or d 5t2

3.5 Continued

- Figure 3.11, p.36
- Horizontal component is always the same
- Vertical component changes
- Resultant diagonal of rectangle formed
- Figure 3.12, p.36
- Initial velocity is greater due to increase in

angle higher path - Figure 3.13, p.36
- Paths of projectiles with same initial speed but

different projection angles. - Projectiles reach different height horizontal

distances. - Distance is the same for projectiles launched at

angles that add up to 90 degrees. - Maximum range or distance is obtained at 45

degree angle - If air resistance is small, it will take the same

amount of time for projectile to reach its max

height as it does to fall - For short range projectiles, assume ground is

flat. - Long range projectiles, account for earths

curvature.

3.6 Fast-Moving Projectiles-Satellites

- Earth Satellite a projectile traveling fast

enough to fall around the earth rather than into

it. - ? This speed is 8 km/s or 18,000 mi/h
- Satellites orbit above earths atmosphere in

order to avoid air drag and burning up. - ?Cant avoid gravity!