Complex Vector Addition Practice Problems
Physics
Name:
Period:
For each of the following questions:
a) Draw a picture showing the way the two vectors add together
b) Break any vectors at angles into x and y components
c) Add the x components to find the total displacement component along that axis
d) Add the y components to find the total displacement component along that axis
e) Add the total x and y components to find the total displacement
Show work for each step.
1. In a pickup football game, a receiver stands right next to the quarterback when the ball is hiked. The
receiver then runs 10 m north, before veering off at a 30° angle to the left (30° W of N) and running an
additional 7 m before they catch the football. What was the receiver’s total displacement from the
quarterback (and the football’s, too) when the ball was caught?
2. A spy stands on the sidewalk by an apartment building examining a foreign embassy across the
street. The spy then climbs 30 m to the top the building and then slides 40 m along a wire at a 20° angle
below right to reach a window on the embassy. What is their total displacement from the sidewalk to
the embassy window?
3. An army tank division leaves base and travels 30 miles at 30° S of W and then turns and travels 70
miles at 10° N of W. What is their total displacement from base at the end of the trip?
4. A spider starts walking from the center of a piece of paper and walks 10 cm at 15° N of W and then
walks 23 cm at 70° S of E before resting. What is the spider’s total displacement from the center to their
resting place?
5. A hiker starts at the base of the trail and hikes 350 m up a slope at a 10° angle above right. They
come to a switchback and head 500 m up a slope at 7° above left. What is the hiker’s total displacement
from the base of the trail when they reach the end of the second leg?