Physics – Vectors Worksheet (#1-18)
1. A track athlete runs 3.5 laps around a circular track. The track has circumference of 4.0 x 102 meters.
(a) Find the distance travelled during the run
(b) Find the magnitude of the displacement after the run.
2. A force of 10.0 pounds acts north and a force of 20.0 pounds acts south. Find the resultant force.
3. A jogger runs 3.0 x 102 meters due east and then 5.0 x 102 meters due south.
(a) What is the total distance that she ran?
(b) What is her total displacement (magnitude and direction)?
4. A plane flying due north at 2.00 x 102 mph encounters winds which blow the plane due south at 45 mph.
Determine the plane's resultant velocity (magnitude and direction).
5. A plane flying due north at 191 mph encounters winds that blow the plane due east at 45 mph. Determine
the plane's resultant velocity (magnitude and direction).
6. Two ropes are attached to a heavy object. The ropes are given to two strong women with instructions to
pull with exactly 1000 lbs of force. What is the magnitude of the resultant force on the object if the two
women pull:
(a) in the same direction
(b) in opposite directions
(c) at right angles to each other
7. A pilot flies a plane 1400 kilometers in a direction 30.0o north of west.
(a) How much farther north is he than when he started?
(b) How much farther west is he than when he started?
8. A boat travels at velocity 45 mph in a direction 20.0o south of west. Find the components of the boat's
velocity.
9. A dog's owner walks 20.0 meters due west and then walks 45o south of west a distance of 150 meters.
Where is he with respect to where he started?
10. A bird flies at 12 mph due west, while at the same time a wind blows the bird at 4.0 mph in a direction
40.0o north of west. Find the resultant velocity of the bird.
11. A plane heads 20.0o north of east at 200 m/s. The wind blows 60o north of east at 50 m/s. What is the
resultant velocity of the plane?
12. A boat heads upstream with a velocity of 40.0 m/s at an angle of 45.0o north of east. The stream flows
with a velocity of 10.0 m/s south. What is the magnitude and direction of the boat's resultant velocity?
13. A man driving a car is exactly 5000 meters due west from the line marking the eastern time zone. He
travels at 30.0 m/s along a straight road that runs in a direction 30.0o north of east. How much time does
it take the man to get to the eastern time zone?
14. A boat heads due east across a stream with a velocity of 20.0 m/s. The stream is flowing from north to
south at a rate of 5.0 m/s.
(a) What is the resultant velocity of the boat?
(b) If the stream is 1.0 x 102 meters wide, what time does it take the boat to reach the other side?
(c) How far downstream is the boat when it reaches the other side?
15. A vector in the xy plane has components -14.0 units in the x-direction and 30.0 units in the y-direction.
(a) What is the magnitude of the vector?
(b) What is the angle between the vector and the positive x-axis?
16. A vector has components Bx = -9.0 units and By = -15 units. Write the vector B in terms of magnitude
and direction.
17. A velocity vector has magnitude 100.0 m/s and make an angle of 160o with the positive x-axis.
Determine the x- and y-components of the vector.
18. A vector is 21 units long, 15o below the positive x-axis. Calculate the components of this vector.