SPH3U1
Solving 2D Motion Questions Algebraically
When two vectors being added are perpendicular, what mathematical skills can be used to solve
for the resultant displacement?
Example 1: A taxi drives 200.0 m [S] and then 120.0 m [E]. Draw a sketch and then solve for
the resultant displacement algebraically. (Remember you will need a magnitude and an angle
with direction)
However, motion is not always perpendicular. 
But don’t worry… we can separate every vector into x and y components (perpendicular
vectors that add to give the original vector) and then solve it as in Example 1.
Draw 2 vectors (one horizontal and one vertical) that can be added so the resultant
displacement is the vector below. These are the x and y components for this vector.
If the original vector is 25m [E 30˚N], calculate the values of the xcomponent and the y-component.
Once all the vectors in a question are broken down into horizontal and vertical components, the
problem can be separated into two linear motion questions. Get the resultant displacement for
all the horizontal vectors. Then do the same for all the vertical vectors. Then solve the question
as in Example 1 using the resultant x-component and the resultant y-component.
Example 2: A taxi drives 280.0 m [N 40˚ E] and then 150.0 m [E 20˚ S]. Draw a sketch and
then solve for the resultant displacement algebraically.
Your Work: Read p.66-74, Complete p.75 #1a-3, 4, 5, 6b, 7,8