Projectile Motion Chapter 3

Vector and Scalar Quantities Nonlinear Motion: motion along a curved path. Magnitude: greatness in size or extent. Vector Quantity: a quantity that requires both magnitude and direction for a complete description. Scalar Quantity: a quantity that is described by magnitude only. (scalars can be +,-,·,÷ just like ordinary numbers)

Velocity Vectors An arrow is used to represent magnitude and direction.This is a vector quantity. Arrow length, drawn to scale, shows magnitude of the vector quantity. The direction of the arrow indicates the direction of the motion.

Velocity Vectors A vector is sometimes the result of combining 2 or more other vectors.

Velocity Vectors

Suppose an airplane flying at 80 km/h encounters wind 60 km/h traveling west to east at a right angle to its forward motion-a crosswind. Will the airplane fly faster or slower than 80 km/h?

Velocity Vectors 80 km/h plane 60 km/h (wind) new direction of plane!

Velocity Vectors

How did we get 100 km/h as our answer? Answer: Whenever a pair of vectors right angles (90°), their resultant can be found by the Pythagorean Theorem. Resultant: the diagonal of the rectangle described by the two vectors.

Velocity Vectors Pythagorean Theorem: a 2 + b 2 = c 2 In our question, what is a 2 ? 60 2 What is b 2 ? 80 2 What is c 2 ? So, the plane will be traveling faster than 80 km/h. Its new velocity will be 100 km/h.

Components of Vectors Components: any vector can be resolved into two component vectors at right angles to each other.

Projectile Motion Ground

Projectile Motion Projectiles: a cannonball shot from a cannon, a stone thrown into the air, a baseball hit by a bat

Projectile Motion At the instant a horizontally pointed cannon is fired, a cannonball held at the cannon’s side is released. Why will the two hit the ground at the same time?

Projectile Motion Because the horizontal vector is constant, and the vertical vector is subjected to 10m/s 2.

Upwardly Launched Projectiles Consider a cannonball shot at an upward angle. Because of gravity, the cannonball follows a curved path and finally hits the ground.

Upwardly Launched Projectiles We can calculate the curve of our projectile by using the equation d = ½gt 2, which can be shortened to d = 5t 2. If we know the angle of the projectile we can calculate at every second the distance between the original curve and the actual curve.

Upwardly Launched Projectiles d = 5t 2 d = 5 × 1 2 d= 5m

Projectile Motion A man on a 5m high hilltop throws a ball 20m before it hits the ground below. At what speed was the ball thrown? 5m 20m

Projectile Motion We know that in d = 5t 2 in 1 second is 5m, hence the ball went 20m/1s. 5m 20m

Fast-Moving Projectiles-Satellites Satellites and the space shuttle actually stay in orbit because they are in a constant state of freefall.