Chapter 3 Projectile Motion

3.1 Vector and Scalar Quantities VECTOR QUANTITIES – quantities that have magnitude and direction EX: force and velocity

3.1 Vector and Scalar Quantities SCALAR QUANTITIES – quantities that have magnitude, but no direction EX: mass, volume, time

MAGNITUDE – strength of something “how much?” DIRECTION – “which way?”

3.2 Vectors vector – represented by an arrow whose length is the magnitude of a physical entity and whose orientation shows how the physical entity is directed.

MAGNITUDE less magnitude more magnitude

DIRECTION EQUAL MAGNITUDE; OPPOSITE DIRECTION

SPEED VS. VELOCITY Velocity has both magnitude and direction. Speed has only magnitude.

You can add the magnitudes of two vectors together to get the magnitude of the resultant vector.

RESULTANT the sum of two or more vectors (and takes into account their directions)

For Example: 200 m/s 300 m/s net velocity or resultant velocity

Also: 100 m/s + 200 m/s 100 m/s net velocity or resultant velocity

For example: 100 km/hr 10 km/hr Net Velocity: 90 km/hr

OR 100 km/hr WIND 10 km/hr Net Velocity: 110 km/hr

Not all vectors occur horizontally. Say the wind was blowing at the plane from the side. WIND

The plane’s velocity is affected by the wind. Crosswind velocity

The plane’s resultant vector would look something like this:

By using the parallelogram method, you can represent the resultant of two vectors.

Geometric Addition of Vectors Parallelograms – shapes that have opposite sides of equal length and are parallel.

EXAMPLES of parallelograms

Create a parallelogram from the two vectors --

then connect the corners. The diagonal is the resultant vector.

Special Case: If you have a 90 degree angle, you can use the Pythagorean Theorem to calculate the magnitude of the resultant.

PYTHAGOREAM THEOREM A2 + B2 = C2 C (hypotenuse) side A side B

For example: 32 + 42 = C2 9 + 16 = C2 ? 3 4 25 = C2 C = 25 C = 5

SOH CAH TOA Sine  = opposite/hypotenuse Cosine  = adjacent/hypotenuse Tangent  = opposite/adjacent You can use these when you are missing the lengths of any of the components.

3.3 Components of Vectors COMPONENT – one of the vectors in a horizontal or vertical direction whose vector sum is equal to the given vector.

3.3 Components of Vectors Resolution – the process of determining the components of a given vector

X X and Y are components (vectors) V is the vector that is resolved V

Y V X Vector V has components X & Y

3.4 Projectile Motion Projectile – any object that is launched by some means and continues in motion by its own inertia EX: a cannonball shot from a cannon a stone thrown in the air a ball rolling off the table

Gravity Gravity acts DOWNWARD A ball moving horizontally is immune to the effects of GRAVITY on its velocity. There is no vertical component, only a horizontal component.

Gravity The instant ball is dropped, gravity acts on it, pulling it toward the center of the earth. Now it only has a vertical component.

3.5 Upwardly-Moving Projectiles Figure 3.10 If a projectile had no gravity acting on it, it would move with this path:

Gravity changes the path of the projectile: Gravity pulls the projectile towards the Earth.

Pathways of Projectiles Objects that move at a constant horizontal velocity while being accelerated vertically down, take a path called a PARABOLA.

PARABOLA

At each point in its path the projectile has velocity vectors such as those below: Each velocity vector has a vertical and a horizontal component.

Acceleration is constant for a projectile. Speed and velocity change at each point along the parabolic pathway. What is the speed of the projectile at the very top of its pathway? What is the acceleration of the projectile at the very top of its pathway?

Air Resistance Air resistance is another force that acts on projectiles. It changes the path of a projectile like this:

Air Resistance IDEAL PATH ACTUAL PATH

Air Resistance If air resistance is negligible, a projectile will rise to its maximum height in the same amount of time it takes it to fall back down.

Air Resistance Without air resistance, the deceleration of the projectile going up is equal to the acceleration of the projectile coming back down.

3.6 Fast-Moving Projectiles: Satellites Satellite – an object that falls around Earth or some other body because of its tremendous speed, instead of falling into it. Page 201

Chapter 3 Key Terms Component Projectile Resolution Resultant Satellite Scalar quantity Vector Vector quantity