Name:___________________
Date:___________________
Physics 11 - Vectors Review
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Answer the following questions showing the formula, number substitution, and your circled final
answer to the correct number of significant figures with the proper units!
1. Find the resultant displacement for a runner who runs:
(a) 42 m east and then 27 m east again.
(1 mark)
(b) 42 m east and then 27 m west.
(1 mark)
2. A hiker leaves camp and walks 10.0 km due north. The hiker then walks 10.0 km due east.
(a) What is the total distance walked by the hiker?
(1 mark)
(b) Determine the resultant displacement walked by the hiker.
(2 marks)
3. A plane flying due north at 100.0 m/s is blown due west at 50.0 m/s by a strong wind. Find the plane’s
resultant velocity.
(2 marks)
4. A 100.0 N force and a 50.0 N force act on point P. The 100.0 N force acts due north. The 50.0 N force
acts due east. What is the magnitude and direction of the resultant force?
(2 marks)
5. A motorboat heads due east 16 m/s across a river that flows due south at 9.0 m/s.
(a) What is the resultant velocity of the boat?
(2 marks)
(b) If the river is 144 m wide, how long does it take the motorboat to reach the other side? (1 mark)
(c) How far downstream is the boat when it reaches the other side?
(1 mark)
6. A boat heads directly across a river 40.0 m wide at 8.0 m/s [E] . The current is flowing at 3.8 m/s [S].
(a) What is the resultant velocity of the boat?
(2 marks)
(b) How long does it take the boat to cross the river?
(1 mark)
(c) How far downstream is the boat when it reaches the other side?
(1 mark)
7. An airplane is headed north with a uniform velocity of 420 km/h and a west wind is blowing east at 77
km/h.
(a) How far from its base will the plane be in 3.0 hours.
(1 mark)
(b) What is its actual direction of flight?
(1 mark)
8. A boy and girl both swim at 3.0 m/s. They jump into a river 1.0 km across with a current of 2.0 m/s
[E].
(a) The boy faces due North at all times. What is his velocity relative to the ground?
(b) The girl swims straight across relative to the shore. What is her velocity relative to the ground?
9. A motorboat is headed [ 30 N of E] with its engine set to move the boat at 30.0 km/h in still water.
There is a current of 15 km/h [S]. What is the velocity of the boat relative to the shore?
10. A pilot wants to fly north. The plane has an air speed of 350.0 km/h. There is a 25.0 km/h wind
blowing to the west.
(a) What is the plane’s ground speed?
(1 mark)
(b) What direction is it heading in?
(1 mark)
11. A pilot flies 300.0 km [E] and then back home 300.0 km [W] at an air speed of 300.0 km/h. A 30.0
km/h wind is blowing to the east.
(a) What is the pilot’s ground speed for each leg of the trip?
(2 marks)
(b) What is the time for each leg of the trip, in minutes?
(2 marks)
(c) How long would the trip take, in minutes, if there were no wind?
(1 mark)
12. Suppose a football player is being pushed by one opponent with a force of 50.0 N [N] and by another
opponent with a force of 120.0 N [E]. What is the resultant of the two forces exerted on the ball
carrier?
(2 marks)
13. Two soccer players kick the ball at exactly the same time. One player’s foot exerts a force of 60.0 N
north. The other player’s foot exerts a force of 80.0 N east. What is the resultant force on the ball?
(2 marks)
14. An airplane flies due west at 120.0 km/h. At the same time, the wind blows it due north at 40.0 km/h.
What is the plane’s resultant velocity?
(2 marks)
15. A weather team releases a weather balloon. The balloon’s buoyancy accelerates it straight up at
15 m / s 2 . A wind accelerates it horizontally at 6.5 m / s 2 . What is the resultant acceleration?
16. A boat is crossing a river. The boat’s velocity is 5.6 m/s (in a direction directly across the stream).
The flowing water carries the boat down stream at a rate such that the resultant velocity of the boat is
6.5 m/s. What is the velocity of the water in the stream?
(2 marks)
17. What is the resultant force on a falling skydiver at an instant when the force of gravity on her is 720 N
and the force of air friction is 480 N?
(1 mark)
18. Two girls are fighting over a boy friend. Mary pulls John toward the north with a force of 80.0 N,
while Gertrude pulls him toward the west with a force of 150.0 N. What is the resultant of the two
forces acting on John? (2 marks)
19. Three ants are struggling to remove the remains of a bee. One ant pushes [N] with a force of 35 N. A
second pushes [E] with a force of 12 N. The third ant exerts a force which exactly cancels the other
two. What is the magnitude and direction of this force? (2 marks)
20. Two horses on opposite sides of a canal are pulling a barge. Each horse pulls with a force of 720 N.
The ropes from each horse come to a common point on the bow of the barge to form an angle of 60.0
with each other. What is the resultant force exerted by the two horses?
67.4 E of N, 100. N 53.1 E of N, 126 km/h 18.4 N of W, 16 m / s 2 23 off vertical, 3.3 m/s directly
down stream, 240 N down, 170. N 61.9 W of N, 37 N toward 250 or 19 W of S, 1200 N forward, 69 m (E), 15 m (E), 20.0 km,
14.1 km 45 E of N, 112 m/s 26.6 W of N, 112 N 26.6 E of N, 18 m/s 29 S of E, 9.0 s, 81 m, 8.9 m/s 25 S of E, 5.0 s, 19 m,
1300 km, 10. E of N, 3.6 m/s 34 E of N, 2.2 m/s N, 26 km/h E, 349 km/h, 4.10 E of N, 330. km/h (E) and 270. km/h (W), 54.5 min and
Assorted Answers: 130. N
66.7 min, 120. min