Math 201-105-RE Exercises
Vectors and Matrices
Navigation Problems
Filename: E18.1) Navigation Problems
Carl F. Gauss
1.
A boat is traveling east across a river at the rate of 4 kilometers per hour while the river’s current is flowing south at a rate of 3
kilometers per hour. Find the resultant velocity of the boat.
2.
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?
3.
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?
4.
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.
5.
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?
6.
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.
Find the ground velocity of the aircraft.
a)
Suppose the pilot has just been made aware of the wind and wishes to correct her course so that she will be actually moving
b)
N60E. In which direction should she steer?
7.
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?
8.
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.
In what direction should the pilot steer?
a)
How long will the flight take?
b)
9.
A river flows from west to east. 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.
If the ferry travels at 12 km/h, what is the speed of the current?
a)
If the trip takes ¼ hour, how far apart are the dock?
b)
Best of Luck !
Steve
ANSWERS:
1.
5 mi. per hour; S53.1E
2.
240 km; (S22.62E)
3.
 2000.6 m/s
4.
 304.14 km/h; N80.5W
5.
 59.1 m
6.
a) 449.04 km/h; N56.2E
b) N63.4E
7.
23.48 km; N15.9W
8.
a) S12.9E
b)  6.45 min.
9.
a)  8.78 km/h
b)  2.69 km