a. The value of v is 9.2
b. The value of u is 9.9
What are vectors?
Vectors are physical quantities that have both magnitude and direction
How to find the value of vectors u and v?
Since we have vectors
- v at 47° to the x-axis and
- w = 10 at 15° to the x-axis,
We resolve them into component form
So, u = -(ucos70°)i - (usin70°)j
u = -(0.3420u)i - (0.9397u)j
v = -(vcos47°)i + (vsin47°)j
v = -(0.6820v)i - (0.7314v)j
w = (wcos15°)i + (wsin15°)j
w = (0.9659w)i + (0.2588w)j
w = (9.659)i + (2.588)j
Since the sum of the three vectors is zero, we have that
u + v + w = 0
u + v = -w
So,
-(0.3420u)i - (0.9397u)j + [-(0.6820v)i - (0.7314v)j] = -[(9.659)i + (2.588)j]
-(0.3420u)i - (0.9397u)j -(0.6820v)i - (0.7314v)j = -(9.659)i - (2.588)j]
-(0.3420u)i -(0.6820v)i - (0.9397u)j - (0.7314v)j = -(9.659)i - (2.588)j]
-[0.3420u + 0.6820v]i - [0.9397u + 0.7314v]j = -(9.659)i - (2.588)j
Equating i components, we have
-[0.3420u + 0.6820v]i = -9.659i
0.3420u + 0.6820v = 9.659
Dividing through by 0.3420. we have
u + 1.994v = 28.242 (1) and
Also, equating j components, we have
- [0.9397u + 0.7314v]j = -2.588j
0.9397u + 0.7314v = 2.588
Dividing through by 0.9397 we have
u + 0.778v = 2.754 (2)
a. The value of v
Subracring equation (2) from(1),we have
u + 1.994v = 28.242 (1)
-
u + 0.778v = 2.754 (2)
2.772v = 25.488
v = 25.488/2.772
v = 9.19
v ≅ 9.2
The value of v is 9.2
b. The value of u
Substituting v into (1), we have
u + 1.994v = 28.242 (1)
u + 1.994(9.19) = 28.242
u + 18.325 = 28.242
u = 28.242 - 18.325
u = 9.917
u ≅ 9.9
The value of u is 9.2
Learn more about vectors here:
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