P H Y S I C S Chapter 2: Two-Dimensional Motion Section 2A: Adding and Resolving Vectors Objectives: 1)We differentiate a scalar and vector 2)We will add and resolve vectors

Scalar vs. Vector Scalar  only magnitude (numerical value) Vector  magnitude and direction Distance Speed Mass Temperature Volume Energy Density Power Work Displacement Velocity Acceleration Force Momentum Weight

Scalar or Vector 1)75.2 degrees 2)55 km west 3) o 4)98.4 m 5)8 m to the left 6)14.0 cm 7)16 km NW 8)25 km/h Scalar Vector Scalar Vector Scalar Vector Scalar

Vectors Represented with an arrow Length = Magnitude Angle = Directionθ

Adding Vectors Rules: added in any order moved maintaining orientation added tip-to-tail 3 m east 4 m north Resultant = 5 m NE

Adding Vectors Which of the following is the correct orientation for adding these two vectors? WRONG RIGHT

Adding Vectors adjacent opposite hypotenuse θ

In-Class Example #1 Tom leaves home and drives 3 km north and then 5 km east to get to work. What is the total distance travelled and his total displacement? ∆x = 5.83 km θ xoxo x

Projectile Projectile: An object thrown/launched and curves due to gravity Path: Trajectory Shape: Parabola

Which hits the ground first? gg

Demo

Which hits the ground first? Motion in the x and y directions are independent of each other

Projectile Motion x-dir motion not affected by gravity (y-dir)

Projectile Motion Gravity (y-dir) not affected by x-dir motion

Determining Hang Time of a Horizontally Launched Projectile If projectile is horizontally launched then v i(y) = 0 Determine y i and y f yo yo   y

Determining the Range of a Horizontally Launched Projectile If projectile is horizontally launched all velocity v i is in x-dir  v i = v i(x) Determine time using y direction v o = v o(x)

In-Class Problem #1 A marble rolls off a table that is 0.85 m high and lands 1.25 m from the base of the table. a) How long was the marble in the air? b) What was the marble’s initial velocity? t = 0.42 s v o = 2.98 m/s