Projectile Motion Chapter 3 Vector and Scalar Quantities

Projectile Motion Chapter 3

Vector and Scalar Quantities • Vector Quantity – Requires both magnitude and direction • Velocity and Acceleration = vector quantities • Scalar Quantity – Requires magnitude only • Scalars can be added, subtracted, multiplied and divided like normal numbers

Velocity Vectors • An arrow is used to represent magnitude and direction of a vector quantity • These arrows may be combined (as in combining two or more velocities) • These are very useful when we get an object (airplane) moving a certain velocity and another (wind) moving at a different velocity

Vector Addition

Components of Vectors • Any vector can be “resolved” into two component vectors at right angles to each other • The process of determining the components of a vector is called resolution

Vector Components

Vector Components

Projectile Motion • Projectiles near the surface of Earth follow a curved path • This path is relatively simple when viewed from its horizontal and vertical component separately • The vertical component is like the free fall motion we already covered • The horizontal component is completely independent of the vertical component • These two independent variables combined make a curved path!

Projectile Motion

Projectile Motion No Gravity With Gravity

Projectile Motion

The Plane and the Package

Upwardly Launched Projectiles • Toss a projectile into the air at some angle; without gravity, the projectile would keep moving further away in a straight-line path • Instead, the projectile is found directly below that point (d = 5 t² to be exact) • Remember that there is no horizontal acceleration, so the projectile always moves equal horizontal distances in equal times • The projectile always lands at the same angle that it was released at

Upwardly Launched Projectiles

Fast-Moving Projectiles —Satellites • What if a ball were thrown so fast that the curvature of Earth came into play? • If the ball was thrown fast enough to exactly match the curvature of Earth, it would go into orbit • Satellite – a projectile moving fast enough to fall around Earth rather than into it (v = 8 km/s, or 18, 000 mi/h) • Due to air resistance, we launch our satellites into higher orbits so they will not burn up

Satellites Launch Speed less than 8000 m/s Projectile falls to Earth Launch Speed equal to 8000 m/s Projectile orbits Earth - Circular Path Launch Speed less than 8000 m/s Projectile falls to Earth Launch Speed greater than 8000 m/s Projectile orbits Earth - Elliptical Path

Assignment • Read Chapter 3 (pg. 28 -39) • Do Chapter 3 Assessment #1946 (pg. 41 -42) • Do Appendix F, Ch. 3 #1 -14 (pg. 663 -665)