1. Vector Example Problems
1. A man walks 10 m to the East. He then walks another 5 m to the
East. What is his resultant displacement? Show with a diagram
(It need not be to scale)
Represent vectors with arrows:
10 m North
5 m North
Resultant, R
R = 15 m North

2. 2. A man walks 40 m to the North (0o), and then turns and walks
30 m to the East (90o). What is his resultant displacement
(magnitude and direction). Draw a sketch.
Navigational bearing:
North, 0o
West, 270o
East, 90o
South, 180o

3. 2. A man walks 40 m to the North (0o), and then turns and walks
30 m to the East (90o). What is his resultant displacement
(magnitude and direction). Draw a sketch. 0o
30 m
270o
90o
40 m R
180o

4. 2. A man walks 40 m to the North (0o), and then turns and walks
30 m to the East (90o). What is his resultant displacement
(magnitude and direction). Draw a sketch.
30 m
To find the magnitude, use the
Pythagorean Theorem:
40 m R
a2 + b2 = c2
( 40 )2 + ( 30 )2 = R R
: magnitude of R

5. 2. A man walks 40 m to the North (0o), and then turns and walks
30 m to the East (90o). What is his resultant displacement
(magnitude and direction). Draw a sketch.
30 m
To find the magnitude, use the
Pythagorean Theorem:
40 m R
a2 + b2 = c2
( 40 )2 + ( 30 )2 = R = R
2500 = R
R =
2500
R = 50 m

6. 2. A man walks 40 m to the North (0o), and then turns and walks
30 m to the East (90o). What is his resultant displacement
(magnitude and direction). Draw a sketch. 0o
30 m
270o
90o
To find the direction, use
SOH-CAH-TOA:
40 m
50 m
180o x
opp 30
tan x = =
= 0.75
adj 40
x = tan -1 ( 0.75 )
= 37o

7. 30 m Reconcile to compass: Navigational bearing = 0 + 37o = 37o 40 m
R = 50 m at 37o
180o

8. 3. A plane flying at 100.0 m/s at 90o encounters a wind blowing
at 30.0 m/s at 180o. Determine the resultant velocity of the plane
(magnitude and direction). Draw a sketch. 0o
100 m/s
270o
90o
30 m/s R
180o
Magnitude:
a2 + b2 = c2
( 100 )2 + ( 30 )2 = R = R = R
R =
10 900
R = 104 m/s

9. 3. A plane flying at 100.0 m/s at 90o encounters a wind blowing
at 30.0 m/s at 180o. Determine the resultant velocity of the plane
(magnitude and direction). Draw a sketch. 0o
100 m/s x
270o
90o
30 m/s
104 m/s
180o
Direction:
opp 30
tan x = =
= 0.30
adj
100
x = tan -1 ( 0.30 )
= 17o

10. R = 104 m/s Reconcile to compass:
90o O
Reconcile to compass:
270o
90o
17O
180o
Navigational bearing = o = 107o
R = 104 m/s at 107o

11. 4. A certain boat can travel at 20.0 km/hr in calm water. The boat is
aimed straight across a river whose current is flowing at 8.0 km/hr.
(a) What is the resultant velocity of the boat?
20 km/hr
Magnitude:
a2 + b2 = c2
8 km/hr
( 20 )2 + ( 8 )2 = R R
464 = R
R =
464
= 22 km/hr

12. 4. A certain boat can travel at 20.0 km/hr in calm water. The boat is
aimed straight across a river whose current is flowing at 8.0 km/hr.
(a) What is the resultant velocity of the boat?
20 km/hr
Magnitude:
a2 + b2 = c2 x
8 km/hr
( 20 )2 + ( 8 )2 = R R
90o – 22o
= 68o
464 = R
R =
464
= 22 km/hr
Direction:
opp 8
tan x = =
= 0.40
adj 20
x = tan -1 ( 0.40 )
= 22o
R = 22 km/hr at 68o to the bank

13. (b) If the river is 1.0 km wide, how long does it take the boat to
reach the other side?
20 km/hr
d = v t
8 km/hr
v v R d
t =
1.0 km v
Use the velocity
of the boat
across the river
1.0 km
t =
20 km/hr
t = hr

14. (c) How far downstream is the boat when it reaches the other side?
20 km/hr
8 km/hr R
d = ?
Use the velocity
of the boat
down the river
d = v t
= ( 8.0 km/hr )( hr )
d = km

15. 5. Determine the resultant of the following force vectors:
A = N at 180o
B = N at 90o
270o
90o
180o R
Magnitude:
a2 + b2 = c2
50 N
( 50 )2 + ( 25 )2 = R
25 N = R
3125 = R
R =
3125
R = N

16. 5. Determine the resultant of the following force vectors:
A = N at 180o
B = N at 90o 0o
270o
90o
55.9 N
Direction:
27o
180o o = 153o
opp 25
tan x = =
= 0.50
adj 50
180o
x = tan -1 ( 0.50 )
= 27o
Navigational bearing = o = 153o
R = N at 153o