Precalculus
Fall Unit 9 – Vectors & Parametric Motion
Vectors – Addition by the Component Method
Oblique Triangles
Name: _____________________________________________________
Date: ______________________ Period: ______________________
To add two or more vectors…
1. Resolve each vector into its and components.
2. Add the corresponding and components.
3. Draw and describe the resultant vector.
a. Use the new and components to find the magnitude.
b. Use the new and components to find the direction angle.
Add using the component method. Round magnitude to the nearest tenth and direction to the
nearest degree.
1.
15 m 45 degrees north of east and 5 m 10 degrees south of east.
2.
25 m 35 degrees south of east and 8 m 60 degrees north of east.
3.
99 m 30 degrees south of west and 15 m 53 degrees north of west.
4.
4 m 75 degrees north of east and 12 m 20 degrees north of west.
5.
62 m 23 degrees south of east and 36 m 45 degrees north of east.
Solve each problem using the component method. Round magnitude to the nearest tenth and
direction to the nearest degree.
6.
A glider is floating through the sky at 45 miles per hour with a heading of 50 degrees north of west
when it meets a head wind of 10 miles per hour blowing 45 degrees south of east. What is its
resultant velocity?
7.
A river boat is crossing the Mississippi River at 12 miles per hour due north. The current in the
mighty Mississippi is 5 miles per hour at 43 degrees south of west. What is the resulting velocity of
the river boat?
8.
A ship leaves port and sails 14 miles at 68 degrees south of west. Then the ship turns due east and
sails 8 miles. How far is the ship from port and what heading would be the shortest way home?
9.
A pilot wants to fly 430 miles per hour at 45 degrees north of east, but there is a westerly wind
blowing 20 miles per hour. What course correction does the pilot have to make to fly on his desired
heading?
10.
A long-distance swimmer starts out swimming a steady 2 miles per hour at 30 degrees south of
west. A 5 mile per hour current is flowing at 10 degrees north of east. What is the swimmer’s
resultant velocity?