Chapter 3 Projectile Motion

What does this quote mean? “Pictures are worth a thousand words.”

3.1 Vector and Scalar Quantities VECTOR QUANTITIES – quantities that have magnitude and direction VECTOR QUANTITIES – quantities that have magnitude and direction EX: Velocity and acceleration

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

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

3.2 Vectors An arrow is used to represent the magnitude and direction of a vector. An arrow is used to represent the magnitude and direction of a vector. –The length is drawn to scale to indicate the magnitude of the vector quantity. –The direction of the arrow indicates the direction of the vector quantity. This arrow is called a vector. This arrow is called a vector.

MAGNITUDE less magnitude more magnitude

DIRECTION EQUAL MAGNITUDE; EQUAL MAGNITUDE; OPPOSITE DIRECTION OPPOSITE DIRECTION

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

Vector vs. Scalar Quantities Vector Quantity Velocity Velocity Acceleration Acceleration Force Force Scalar Quantity Speed Speed Mass Mass Time Time Volume Volume Temperature Temperature

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

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

For Example: 100 m/s m/s m/s 200 m/s 300 m/s net velocity 300 m/s net velocity or resultant velocity or resultant velocity

Also: 100 m/s 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 10 km/hr Net Velocity: 110 km/hr WIND Windy City

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. Plane’s velocity Crosswind velocity

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

By using the parallelogram method, you can represent the resultant of two vectors. 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. 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. If you have a 90 degree angle, you can use the Pythagorean Theorem to calculate the magnitude of the resultant.

PYTHAGOREAM THEOREM A 2 + B 2 = C 2 side A side B C (hypotenuse)

For example: = C = C 2 4 ? 25 = C 2 C = 25 C = 5

Solve: A plane is flying west at 150 mph and meets a crosswind moving at 120 mph north. At what velocity is the plane actually moving? A plane is flying west at 150 mph and meets a crosswind moving at 120 mph north. At what velocity is the plane actually moving? HINT: Remember velocity is a VECTOR quantity. HINT: Remember velocity is a VECTOR quantity.

C 2 = A 2 + B 2 C 2 = A 2 + B 2 C 2 = (120) 2 + (150) 2 C 2 = (120) 2 + (150) 2 C 2 = C 2 = C 2 = C 2 = C = √(36900) C = √(36900) C = mph, NW C = mph, NW Plane 150 mph Win d 120 mph

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.

Solve: If a plane is flying at 30° NE of the horizontal, what are the two components that make up this resultant vector? If a plane is flying at 30° NE of the horizontal, what are the two components that make up this resultant vector?

Cos (30°) = x/70 Cos (30°) = x/70 70 * Cos (30°) = x 70 * Cos (30°) = x 60.6 mph = x 60.6 mph = x Sin (30°) = y/70 Sin (30°) = y/70 70 * sin (30°) = y 70 * sin (30°) = y 35.5 mph = y 35.5 mph = y 70mph 30° x y

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. 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 Resolution – the process of determining the components of a given vector

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

Vector V has components X & Y X Y V Surfing

3.4 Projectile Motion Projectile – any object that is launched by some means and continues in motion by its own inertia 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 stone thrown in the air a ball rolling off the table 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 the ball is dropped, gravity acts on it, The instant the ball is dropped, gravity acts on it, pulling it toward the center of the earth. 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: 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 Gravity pulls the projectile towards the Earth. 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. 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. Hang Time Revisited

Acceleration is constant for a projectile. Acceleration is constant for a projectile. Speed and velocity change at each point along the parabolic pathway. 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 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? 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. 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. 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. 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 Component Projectile Projectile Resolution Resolution Resultant Resultant Satellite Satellite Scalar quantity Scalar quantity Vector Vector Vector quantity Vector quantity