1. Vectors: Word Problems
Pre-Calculus

2. Review:
Magnitude represents distance… in word problems this is often speed or force, etc…
Θ is our angle, which represents direction…
IT IS ALWAYS POSITIVE!

3. DRAW THE VECTOR AND GIVE THE ANGLE,θ, THAT WOULD BE USED TO FIND THE COMPONENT FORM.
Ex 1) 30° east of south Ex 2) 50° west of north
Ex 3) 25° east of north Ex 4) 60° west of south

4. When looking for resultant speed & direction, you will be using vector addition of the two vectors involved.
This is when “tip to tail” is important! v u
u + v
This is the resultant vector

5. After the vector addition, you will use the component form of resultant vector to find speed (distance) and direction (θ).
When drawing the diagram for the word problem, remember to use the POSITIVE value of θ.
Directional Bearings are given in NE, SE, NW or SW headings.

6. Ex 5) Superman flies due west at 250 km per hour while the wind blows south at 70 km per hour. Find his resultant velocity and direction.

7. Ex 6)

8. Ex 7)

9. Ex 8) A motorboat is heading N 10° E at 260 mph
Ex 8) A motorboat is heading N 10° E at 260 mph. A 16 mph wind blows from the west. Find the boats resultant velocity and direction.

10. Ex 9) An airplane flies east 210 km before turning S 20° E and flying 100 km. Find the distance and direction of the plane from its starting point.

11. Ex 10) An airplane is traveling in the direction of 20° west of north at a speed of 325 mph. A wind is blowing in the direction of 50° west of north at 40 mph. Find the planes resultant velocity and direction.