Vectors as Component Practice and Application
In using ground speed, we mean the resulting speed of the plane as observed form the
ground after the effect of the wind. For example, if a plane travels 620 mph into a head
wind of 20 mph, its ground speed is 600 mph.
1. Given a vector w with magnitude 12 and direction 142°, give its component form.
2. An airplane has an airspeed of 520 mph and a bearing of 115°. The wind blows from
the east at 37 mph. Find the plane’s ground speed and bearing.
3. A pilot wants his plane to head N 20°W at 500 mph (ground speed). There is a wind
blowing S 10° E at 45 mph. What direction should he head and at what airspeed? Draw a
picture of this situation and set up a vector equation before you solve this problem.
4. A fishing boat leaves port and travels at a constant rate of 15 knots, heading N 20 E
for 6 hours. It then changes course to N 30 W for 4 hours. Finally it changes course to
N 10 W for 10 hours. At this point, the fishermen have a complete catch and wish to
return directly to port. What direction should they head and how long does it take them?
5. A ferry boat leaves the east bank of the Mississippi River with a compass heading of
300° and is traveling 10 mph relative to the water (speed in still water). Assuming the
river is running directly south at this point at 4 mph, determine the boats actual course,
the time it takes the cross the river if it is ½ mile wide, and how far up or downstream it
lands.
6. Determine the magnitude and resulting direction of the answer to the following:
12,  3  2 3,7  6 8,10
7. Vector A makes a 39° angle with the positive x-axis and has a magnitude of 60. It is
added to vector B that makes a 125° angle to the positive x-axis with a magnitude of 27.
a. Determine the magnitude and direction of the sum A  B .
b. Find the magnitude and direction of the vector C such that A  C  B .