Math 201-NYC-05 Exercises
Vectors and Matrices
Navigation Problems
Filename: E16.2) Navigation Problems.Doc
Carl F. Gauss
1.
A force of 12 pounds is applied to an object along the negative x-axis and a force of 5 pounds is applied to the same object
along the positive y-axis. Find the magnitude and direction of the resultant force.
2.
A boat is traveling east across a river at the rate of 4 miles per hour while the river’s current is flowing south at a rate of 3 miles
per hour. Find the resultant velocity of the boat.
3.
A ship is being pushed by a tugboat with a force of 300 pounds along the negative y-axis while another tugboat is pushing
along the negative x-axis with a force of 400 pounds. Find the magnitude and sketch the direction of the resultant force.
4.
An airplane is flying with an air-speed of 260 kilometers per hour while a wind is blowing to the west at 100 kilometers per
hour. Indicate on a figure the approximate direction that the plane must follow to result in a flight directly south. What will be
the resultant speed?
5.
A rocket moving away from the earth at 2,000 m/s releases an instrument package at right angles to its direction of motion. If
the speed of the package is 50 m/s as seen from the rocket, what is the velocity of the package as seen from the earth?
6.
An airplane has an air-speed of 300 km/h and is headed due west. A wind is blowing from the south at 50 km/h. Find the
ground velocity of the plane.
7.
A cruise ship sails west. A passenger on deck walks S10E (i.e. 10 east of south) In the time it takes the passenger to walk 10
m on deck, the ship has sailed 60 m. How far has the passenger actually moved with respect to the water?
8.
An aircraft is flying at an air-speed of 500 km/h, steering 60 east of north (i.e. N60E). A 60 km/h wind is blowing from the
east.
a) Find the ground velocity of the aircraft.
b) Suppose the pilot has just been made aware of the wind and wishes to correct her course so that she will be actually
moving N60E. In which direction should she steer?
9.
A fisherman wishes to cross a river from A to B as shown in the diagram. His outboard
motor produces a speed of 20 km/h but there is a current of 8 km/h as shown. In which
direction should he steer and what will be his actual speed?
23.48 km; N15.9W
10.
A pilot wishes to fly from A to B. The distance is 40 km, and B is S20E from A. The cruising speed of the aircraft is 350
km/h, but there is a 50 km/h wind blowing from N80W.
a) In what direction should the pilot steer?
b) How long will the flight take?
11.
A river flows from west to est. There are ferry terminals on the north and south shores, the north dock being 15 east of north
(i.e. N15E) from the south dock. The ferry captain knows from experience that in order to reach the dock on the north shore
from the south shore dock, she has to steer N30W.
a) If the ferry travels at 12 km/h, what is the speed of the current?
b) If the trip takes ¼ hour, how far apart are the dock?
Best of Luck !
Steve
ANSWERS:
1.
4.
7.
13 pounds; 22.6 North of West
240 km; (S22.62E)
 59.1 m
2.
5.
8.
10.
a) S12.9E
b)  6.45 min.
11.
5 mi. per hour; 36.9 South of E
 2000.6 m/s
a) 449.04 km/h; N56.2E
b) N63.4E
a)  8.78 km/h
b)  2.69 km
3.
6.
9.
500 pounds; S53.13W
 304.14 km/h; N80.5W
23.48 km; N15.9W