Add the two component vectors from Sample Problem 1 algebraically to erify that they equal the given vector
The two component vectors are:
8.6m(North) and 12m (west)
The given vector is 15m(West 35 degrees North)
To add the two component vectors algebraically, we need to break them down into their x and y components.
The vector 8.6m (North) can be represented as:
x-component: 0m (since it is purely vertically)
y-component: 8.6m
The vector 12m (West) can be represented as:
x-component: -12m (since it is purely horizontally to the left)
y-component: 0m (since it is purely horizontally)
Now, we can add the x and y components separately:
Adding the x-components:
0m + (-12m) = -12m
Adding the y-components:
8.6m + 0m = 8.6m
Therefore, the resulting vector from adding the two component vectors algebraically is:
-12m (West) + 8.6m (North)
To check if this is equal to the given vector 15m (West 35 degrees North), we need to convert the given vector into its x and y components.
The given vector 15m (West 35 degrees North) can be represented as:
x-component: -15m * cos(35°) ≈ -12.23m
y-component: 15m * sin(35°) ≈ 8.60m
Comparing the x and y components:
x-component of the resulting vector (-12m) is approximately equal to the x-component of the given vector (-12.23m).
y-component of the resulting vector (8.6m) is approximately equal to the y-component of the given vector (8.6m).
Therefore, the resulting vector from adding the two component vectors algebraically is approximately equal to the given vector 15m (West 35 degrees North).