1
HW 2 VECTORS - COMPONENTS
1. Carefully construct and calculate the vertical and horizontal components of the following vectors:
a.
v
= 3m/s, 300
v x  v cos 
v  ( 3 m / s ) cos 30 0
x
vx = 2.6 m/s
b.
v = 3m/s, 450
c. F = 3N, 1200
d. 𝑥⃗ = 3m, 2100
e. 𝑎⃗ = 4m/s2, 3000
v y  v sin 
v y  ( 3m / s ) sin 30 0
vy = 1.5 m/s
2
2. Carefully construct and calculate the magnitude and direction of the vectors that has following horizontal and vertical components:
a. vx = 45 m/s , vy = 30 m/s
v  vx2  v 2y
  arctan
b. vx = 30 m/s , vy = 45 m/s
c. Fx = - 30 N , Fy = 45 N
d. xx = 110 m,
xy = - 150 m
e. ax = - 110 m/s2 , ay = -150 m/s2
30
45
v  ( 45 m / s ) 2  ( 30 m / s ) 2  2925 m 2 / s 2
θ = 340
v  54m / s @ 340
v = 54 m/s
3
3.
Find the resultant
v
if
v
1 = 3 m/s, N;
v2
Calculate magnitude and direction of the vector
a.
v  v v
1
2
= 4 m/s, E ;
v
:
magnitude: v  v 2  v 2
1
2
direction:   arctan
v1
v2
v  32  42
3
  arctan
4
v = 5 m/s
v  5m / s @ 370
 = 370
b. v  v1  2v 2
c.
v  2v  v
1
2
d. v  v 1  2v 2
4.
Find
F
(magnitude F and direction ) if F1 = 6 N, 00;
Draw vector
a. F  F1  F2
F2 = 6 N, 1200;
F3 = 6 N, 600
F
b. F  F1  F3
c. F  F3  F2
4
0
5. Draw and add three vectors: F 1  ( 40 N ,0 )
Find resultant force!
0
F 2  ( 30 N ,180 )
0
F 3  ( 50 N ,90 )
6. A northeast and a southeast vector are being added using the parallelogram method. Which diagram below illustrates the correct method
of adding two such vectors.
7. Use the following vectors to answer the questions.
a. Which vectors have the same magnitude?
b. Which vectors have the same direction?
c. Which arrows, if any, represent the same vector?
5
1. a.
v x  v cos 
v y  v sin 
b.
d.
vx = 2.6 m/s
vx =- 2.6 m/s
vy = 1.5 m/s
vy = -1.5 m/s
vx = (3 m/s) cos
c.
e.
300
= 2.6 m/s
vx = -1.5 m/s
vx = 1.5 m/s
vy = (3 m/s) sin
300
= 1.5 m/s
vy = 2.6 m/s
vy = -2.6 m/s
2. b.
vx = 30 m/s , vy = 45 m/s
v  ( 30 m / s ) 2  ( 45 m / s ) 2  2925 m 2 / s 2
  arctan
45
30
 = 560
v = 54 m/s
v = 54m/s @ 56 0
c.
vx = - 30 m/s , vy = 45 m/s
v  ( 30 m / s ) 2  ( 45 m / s ) 2  2925 m 2 / s 2
  90 0  arctan
30
45
v = 54 m/s
v  54m / s @ 127 0
= 1270
d.
Fx = 110 N,
Fy = - 150 N
F  F  F2  F2
F  (110 N ) 2  (150 N ) 2  34600 N 2 F =186 N
 150 
  arctan  

 110 
 = -540
x
y
F  186 N @ -5 40
e.
Fx = - 110 N ,
Fy = -150 N
F  F  F2  F2
x
  1800  arctan
3.
v
1 = 3 m/s, N;
v2
  arctan
3
8
150
110
c.
v  32  82
 = 210
v  8.5m / s @ 210
F  186 N @ 234 0
 = 2340
= 4 m/s, E ;
b. v  v1  2v 2
v  v 12  v 22
F  (110 N ) 2  (150 N ) 2  34600 N 2 F =186 N
y
v = 8.5 m/s
v  2v  v
1
2
v  42  6 2
v  v 12  v 22
  90 0  arctan
4
6
= 1240
v  7.2m / s @ 124 0
v = 7.2 m/s
6
d. v  v1  2v 2
v  32  82
v  v 12  v 22
v = 8.5 m/s
3
8
 = 2010
F2
= 6 N, 1200;
  180 0  arctan
v = 8.5m/s @ 2010
4. Find:
F
(Magnitude F and direction) if
F F F
1
F F F
2
F  6 N @ 600
F = 6 N, 00;
1
1
= 6 N, 600
F  F  F
3
3
F  10.4 N @ 3 00
0
5. Draw and add three vectors: F 1  ( 40 N ,0 )
Find resultant force!
F3
2
F  6 N @ 18 00
F 2  ( 30 N ,180 0 )
F 3  ( 50 N ,90 0 )
F  F1  F 2  F 3
F  102  502 = 51 N
 = arc tan (50/10) = 790
F  51N @ 790
6. Use the following vectors to answer the questions.
a. Which vectors have the same magnitude?
A,C , E , H and I
b. Which vectors have the same direction?
A,D,H
c. Which arrows, if any, represent the same vector?
;
B,C ,G
A and H
I,J