Projectile MotionProjectile Motion

Chapter 3Chapter 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

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

Velocity Vectors

• How did we get 100 km/h as our answer?• Answer: Whenever a pair of vectors are @ 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: a2 + b2 = c2

• In our question, what is a2 ?• 602

• What is b2 ?• 802 • What is c2 ?• 1002 • 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/s2 .

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 = ½gt2 , which can be shortened to d = 5t2 . 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 = 5t2

d = 5 × 12

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 = 5t2 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.