Vectors II
1. A person leaves home and walks 4 miles west, then 2 miles southwest.
How far from home is she?
In what direction must she walk to head directly home?
__________________ degrees North of East
2. Match the vectors
with one of the combinations of
the and vectors from the graph.
Vector

____
a.

____
b.

____
c.

____
d.

____
e.
3. Write the vector shown below as a combination of vectors
Vector = __________________
Vector Combination
+ __________________
Note: In both graphs, each box is 1 unit by 1 unit in size
and shown above
4. An airplane needs to head due north, but there is a wind blowing from the
northwest at 50 km/hr. The plane flies at an airspeed of 800 km/hr,
To end up due north, the pilot will need to fly the plane __________________
degrees west of north
5. A person starts walking from home and walks:
4 miles East
2 miles Southeast
6 miles South
2 miles Southwest
3 miles East
This person has walked a total of __________________ miles
Find the total displacement vector for this walk: __________________ +
__________________
If this person walked straight home, they'd have to walk __________________
miles
6. An airplane is heading north at an airspeed of 650 km/hr, but there is a wind
blowing from the southwest at 60 km/hr.
The plane will end up flying __________________ degrees off course
The plane's speed relative to the ground will be __________________ km/hr
7. Write the vector shown in component form.
Vector = __________________ + __________________
Note: In the graph, each box is 1 unit by 1 unit in size
8. A vector with magnitude 3 points in a direction 235 degrees counterclockwise
from the positive x axis.
Write the vector in component form.
Vector = __________________ + __________________
9. Given the vector
, find the magnitude and angle in which the vector
points (measured counterclockwise from the positive x-axis,
)
= __________________
= __________________
10. For the following vector, convert from magnitude and direction to x and y
coordinates
x = __________________, y = __________________
11. For the following vector, convert from magnitude and direction to x and y
coordinates
x = __________________, y = __________________
12. For the following vector, convert from x and y coordinates to magnitude and
direction
r = __________________, = __________________
13. For the following vector, convert from x and y coordinates to magnitude and
direction
r = __________________, = __________________
14. A Ferry shuttles people from one side of the river to the other. In still water the
ferry's speed is 20 mi/h and the river flows directly south at 5 mi/h. Suppose the
ferry heads directly west. what is the ferry's speed and direction?
Speed = __________________ mi/h
Direction = __________________ degrees South of West
15. Find the magnitude and angle (in degrees) of the vector shown.
Magnitude: __________________
Angle: __________________ degrees
16. A red cross helicopter takes off from headquarters and flies 135 km at 35
degrees south of west. There it drops off some relief supplies, then flies 140 km
at 10 degrees west of north to pick up three medics.
If the helicoper then heads directly back to headquarters, find the distance and
direction it should fly.
Distance: __________________ km
Direction: __________________ degrees
+++++++++++++++Key - Form 1
1. 5.5958653038636 ~ 14.638806595178
2. d b c a e
3. -1 ~ 3
4. 2.5329646286916
5. 17 ~ 7 ~ -8.8284271247462 ~ 11.266815233106
6. 3.5062482276402 ~ 693.72496634657
7. -3 ~ 4
8. -1.7207293090531 ~ -2.457456132867
9. 3.1622776601684 ~ 3.4633432079864
10. 2.5711504387462 ~ 3.0641777724759
11. 1.7320508075689 ~ -1
12. 7.211102550928 ~ 56.30993247402
13. 8.4852813742386 ~ 135
14. 20.615528128088 ~ 14.036243467926
15. 4.1231056256177 ~ 75.963756532074
16. 147.81755547364 ~ 24.134762771598 ~ South of East