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Elective Physics 10 Vectors Worksheet : Vector Operations
1
2A
-B
1.
-A 2B
-B+2A
2B-A
-B
A
A-B
a) c)
b)
Elective Physics 10 Vectors Worksheet : Vector Operations
2
2.3A
B
-C 3A+B-C
-2A
BC
B+C-2A
a)
b)
Elective Physics 10 Vectors Worksheet : Vector Operations
3
3.
C-2B
-C
-2B B-B
-B
A+BA
a)2B -A
2B-A
b)
c)
BC
B+C
Elective Physics 10 Vectors Worksheet : Vector Operations
4
4.
A
B
C DE
R
R 2 = 22 +42 ⇒ R 2 = 4+ 16R 2 = 20⇒ R = 2 5 cm
4 cm
2 cm
R
Elective Physics 10 Vectors Worksheet : Vector Operations
5
5.
B
A
C
D
R
E
E
E2 = 22 +42 ⇒E2 = 4+ 16E2 = 20⇒E = 2 5 cm
4 cm
2 cm
Elective Physics 10 Vectors Worksheet : Vector Operations
6
6.
-CB+C
B
a) the magnitude of
vector B is 2 cm
b)B
A+B
Athe magnitude
of vector A is
4 cm
Elective Physics 10 Vectors Worksheet : Vector Operations
7
7.
A-BO
A+B 2A
2A A
The magnitude of
vector A is 2 cm
Elective Physics 10 Vectors Worksheet : Vector Operations
8
8.
A+B B+C
A+C
2A+2B+2C
A+B+C
R
Elective Physics 10 Vectors Worksheet : Vector Operations
9
9.
3 m1 m
2 m
2 m
2 m2 2 m
2 2 m
45o
45o
Step-1
Step-2
Step-3
45o
2 2 m
2 2 m
45o
4 m 4 m
4 m
Step-4
R=4 m
60o
60o60o
Elective Physics 10 Vectors Worksheet : Vector Operations
10
10.
A
6 N
3 N
3 N120o 120o
Step-1 : divide vector A into two equal vectors.
Step-2
3 N 120o
3 N
3 N
Step-3
60o
3 N
60o60o
3 N
60o60o
3 3 N
3 3 N
3 3 N
R=9 NStep-4
+x
+y
Elective Physics 10 Vectors Worksheet : Vector Operations
11
11.
8 N 8 N
8 N
+y
+x
Step-1
60o60o
120o
Step-2
12 N
+x60o
60o
+y
60o
4 3 N 4 3 N
Step-3
8 N
12 N
4 N
Step-4
4 N
3 N
R=5 m
Elective Physics 10 Vectors Worksheet : Vector Operations
12
12.
East
North
West
South
53o
A
B
20 m
4 m
-B
4 m Ax
Ay
Ax=A.cos53o=(20).(0,6)=12 m
Ay=A.sin53o=(20).(0,8)=16 m
x-component y-component
A
-B
R
+12 m +16 m
0 -4 m
+12 m +12 m
12 m
12 m
R
Rx
Ry
R = 12 2 m
Elective Physics 10 Vectors Worksheet : Vector Operations
13
13.
East
North
West
South
53o
BA
C20 paces
15 paces 25 paces
Bx=B.sin53o=(25).(0,8)=20 paces
By=B.cos53o=(20).(0,6)=15 paces
x-component y-component
C
A
B
0 +15 paces
+20 paces +15 paces
+20 paces 0
R +40 paces +30 paces
30 paces
40 paces
R
Rx
Ry
R=50 paces
Elective Physics 10 Vectors Worksheet : Vector Operations
14
14.
Bx=B.cos53o=(20).(0,6)=12 N
By=B.sin53o=(20).(0,8)=16 N
Ax=A.cos37o=(10).(0,8)=8 N
Ay=A.sin37o=(10).(0,6)=6 N
x-component y-component
A
B
R
-8 N -6 N
+12 N +16 m
+4 N +10 N
R 2 = 42 + 102
R 2 = 16+ 100R 2 = 116⇒
R = 2 29 N
Elective Physics 10 Vectors Worksheet : Vector Operations
15
15. 3 N + 4 N < 8 N
So these vectors cannot form a triangle. Then the magnitude of the resultant vector cannot be equal to
zero.
16.x-component y-component
a
b+2a
-1 -1
+2 +2
-2 0
-2a
b
(-2a)(b+2a)+ = b
0 +2
So, vector “b” is “2”.
Elective Physics 10 Vectors Worksheet : Vector Operations
16
17.x-component y-component
2a
2 0
-1 -2
+1 -2
c-2a
a-b
+ =
0 +2
So, vector “c” is “3”.
a+b
(a+b) (a-b) 2a
2a +(c-2a)= c
c +1 0
Elective Physics 10 Vectors Worksheet : Vector Operations
17
18.
=0(K+L+M)
=M -(K+L)
So “4” is the vector “M”.
Elective Physics 10 Vectors Worksheet : Vector Operations
18
19.Vectors N and L are in the same line of action. So,
their resultant vector has a magnitude of 4 m and it is in the same direction as vector N.
Vectors K and M are in the same line of action. So, their resultant vector has a magnitude of 15 m and it
is in the same direction as vector M.
We can use the law of cosines to add these two vectors by using tip-to-tail method. The angle between them
is 530.
R2=(4)2+(15)2-(2.4.15.cos 530)
R2=(16)+(225)-(120.(0,6))
R2=(241)-(72))
R2=169
R=13 m
Elective Physics 10 Vectors Worksheet : Vector Operations
19
20.
R=F1+F2+F3
F2+F3 =F1
R=F1+F1=2F1
R=2F1=2F
21.R=K-L+M-N+P
R=-N-N=-2N
K-L+M+P =-N
Elective Physics 10 Vectors Worksheet : Vector Operations
20
22.
4 N and 6 N are in the same line of action. So, their resultant vector has a magnitude of 2 N
and it is in the same direction as 6 N.
3 N and 5 N are in the same line of action. So, their resultant vector has a magnitude of 2 N
and it is in the same direction as 5 N.
45o 45o
2 N2 N
2 N
2 N
(2 2)2
R
R2=(2)2+
R2=4+8=12
R=2 3 N
2 2 N
Elective Physics 10 Vectors Worksheet : Vector Operations
21
23. F3
F2F1
F4a
F4.cosa+F1=F3
F4.sina
F4.sina=F2 then F4>F2
Only statement-II is absolutely correct.
For statements I & III, we cannot say anything about being absolutely correct.
If R=0 then
Elective Physics 10 Vectors Worksheet : Vector Operations
22
24.
-F2-F3
F3 +2F2
F2
F2+F3
-F2
F3
F3=2 2 units
Elective Physics 10 Vectors Worksheet : Vector Operations
23
25.
99 N
99 N
99 N
1200
1200
1200
R=0
1 N
2 N
12006001 N 2 N
R
R2=(1)2+(2)2-(2.1.2.cos600)
R2=(1)+(4)-(2.1.2.(1/2))
R2=(5)-(2)
R2=3
R= 3 N
by using the law of cosines;
Elective Physics 10 Vectors Worksheet : Vector Operations
24
26.
b + d = 0
a = c
R = 2a or R=2c
27.
3 N
4 N
8 N
6 N
3 N
4 N
R
R=5 N
Elective Physics 10 Vectors Worksheet : Vector Operations
25
28.
12 N
37o
53o
15 N
12 N
9 N
a
21 N
21 N
R
R=21 2 N
x
cos530=a/x
53o
12 N
a
x
53o
sin530=12/x
3/4=a/12
a=9 N
0,6
0,8
Elective Physics 10 Vectors Worksheet : Vector Operations
26
29.
a + b + c + d = e
R = 2e
R = a + b + c + d + e
30.
20 - 10 = 10 N
the angle between 10 N & 10 N is 1200.
their resultant is 10 N upward (to +y)
R=30-10=20 N (to -y)
Elective Physics 10 Vectors Worksheet : Vector Operations
27
31.x-component y-component
M
+2 0
0 +1K
-1 -1
-K+L
+1 +1
L +2 +1
K+L+M
So, the vector “5” is the resultant vector of K+L+M
Elective Physics 10 Vectors Worksheet : Vector Operations
28
32.
R1= 3 F1 R2= 2 F2 R3=F3
The magnitudes of the resultant forces of the given forces are
R1= R2= R3
3 F1 2 F2 F3= =
F3 F2 F1> >
Elective Physics 10 Vectors Worksheet : Vector Operations
29
33.
The magnitudes of the two vector that are added are equal to each other.
If the angle between them gets smaller, the magnitude of their resultant vector would be
greater.
R3 R2 R1> >
34.
Rmax = A+B=10 m
Rmin = A-B=2 m
A = 6 m
B = 4 m
Elective Physics 10 Vectors Worksheet : Vector Operations
30
35. K
L
-P
-M
N
I.
Correct
II.
-LWrong
N-L=-PCorrect formIII. -K
M
P
-N
Correct
N-L=P
-M
Statements I and III are correct
Elective Physics 10 Vectors Worksheet : Vector Operations
31
36.a
b
3c/2
d
The sum of vectors “a” and “b” is equal to “3c/2”. Statement I is wrong.
Vectors “b” and “d” are in different directions but their magnitudes are equal. Statement II is
correct.
b
c
The sum of vectors “b” and “d” is equal to vector “c”. Statement III is correct.
Statements II and III are correct.