Two Dimensional Motion

• we will now analyze motion in the horizontal plane which (like all planes) is two dimensional

• we will first use vector diagrams to answer questions and follow that up with answering questions mathematically

Vector Quantity• any quantity that is described by a number, a unit, and a direction• common vector quantities are displacement, velocity, acceleration, and force

Quick review of vector diagrams:1. select a scale (relationship between vector and quantity) and directional compass.2. draw a reference origin.3. draw a line segment of appropriate length and direction4. draw the arrowhead at the tip5. label the vector

Draw the following vector: = 700 m [E]

N

1 cm = 100 m�⃑�

1.3 Prac. #1

Adding Vectors • draw vectors to scale in the appropriate direction, connecting them tip to tail.• draw the resultant vector from the tail of the first vector, to the tip of the second

vector• measure the length of the resultant vector and use the scale to determine the

magnitude of the vector• use a protractor to determine the direction of the vector• label the vector

ALWAYS ADD THE NEXT VECTOR WHERE THE PREVIOUS VECTOR FINISHED

Resultant Displacement • displacement is the change in position of an object• resultant displacement (dR) is the vector sum of the individual

displacements (d1 + d2 + d3 + …)

1. Andrew rides his bike 3.0 km [W] and then heads goes 7.0 km [S]. Calculate his resultant displacement.

N

1 cm = 1 km�⃑�1

�⃑�2 �⃑�𝑅

= 3.0 km [W] = 7.0 km [S] = ?

= 7.5 km [65˚ S of W] [25˚ W of S]

2. John rides his skateboard 3.0 km [W], then heads 5.0 km [S] and finally turns 6.0 km [E]. Calculate his resultant displacement.

= 3.0 km [W] = 5.0 km [S] = 6.0 km [E] = ?

�⃑�1

�⃑�2 �⃑�𝑅

N

1 cm = 1 km

�⃑�3 = 6.0 km [30˚ E of S] [60˚ S of E]

1.3 Prac. #2,3