need help combining these vectors (if you can please show me a step by step guide of combining these two. Thank you
56m at 296 degrees, then 83m 152 degrees
easy. However, you have to know from whence the angles are measured. I will assume the N axis. So my East axis is at angle 90, W is at 270. IT matters.
56@296+83@152
Notice the N component is a cosine angle function, E is a sine function.
56cos296 N + 56sin296 E+83Cos152 N+83sin152 E
if you have a -E, you can later change it to W, and the same for -N, you can change it to S.
i got an answer of 50meters at 13degrees
do i have to add anything like north of east since it did not give me a direction on the questions
To combine these two vectors, we need to find the resultant vector by adding their horizontal components and vertical components separately. Here's a step-by-step guide on how to combine the given vectors:
1. Convert the vectors from polar form to rectangular form using the following formulas:
- For the first vector (56m at 296 degrees):
horizontal component = magnitude * cos(angle)
vertical component = magnitude * sin(angle)
- For the second vector (83m at 152 degrees):
horizontal component = magnitude * cos(angle)
vertical component = magnitude * sin(angle)
2. Calculate the horizontal components:
- For the first vector: horizontal component = 56m * cos(296 degrees)
- For the second vector: horizontal component = 83m * cos(152 degrees)
3. Calculate the vertical components:
- For the first vector: vertical component = 56m * sin(296 degrees)
- For the second vector: vertical component = 83m * sin(152 degrees)
4. Add the horizontal components:
- Total horizontal component = horizontal component of the first vector + horizontal component of the second vector
5. Add the vertical components:
- Total vertical component = vertical component of the first vector + vertical component of the second vector
6. Calculate the magnitude of the resultant vector using the Pythagorean theorem:
- Magnitude of the resultant vector = sqrt((Total horizontal component)^2 + (Total vertical component)^2)
7. Calculate the angle of the resultant vector using the inverse tangent function:
- Angle of the resultant vector = arctan(Total vertical component / Total horizontal component)
Once you have calculated the magnitude and angle of the resultant vector, you can convert it back to polar form if desired.