The displisacement from A to B is 36 miles at 12 degress N of West. The displacement from B to C is 39 miles at 21 degrees N of E. What is the displacement from A to C by graphical means and by compnents?

To find the displacement from A to C using graphical means, we can draw a diagram. Let's start by plotting the displacement from A to B.

1. Draw a line segment representing the displacement from A to B, which is 36 miles.
2. Draw an arrow pointing in the 12 degrees North of West direction.

Next, let's plot the displacement from B to C.

3. Starting from the end point of the displacement from A to B, draw another line segment representing the displacement from B to C, which is 39 miles.
4. Draw an arrow pointing in the 21 degrees North of East direction.

Now, to find the displacement from A to C, we need to connect the starting point (A) to the ending point (C) of the diagram.

5. Measure the length of this final displacement using a ruler, and record it as the graphical displacement from A to C.

To find the displacement from A to C by components (using vector addition), we can break down the displacements into their North and West components.

Let's calculate the North (N) component of the displacement from A to B:
N_A to B = 36 miles * sin(12 degrees) = 7.4 miles

And the West (W) component of the displacement from A to B:
W_A to B = 36 miles * cos(12 degrees) = 34.7 miles (rounded to one decimal place)

Now, let's do the same calculations for the displacement from B to C:
N_B to C = 39 miles * sin(21 degrees) = 13.4 miles
W_B to C = 39 miles * cos(21 degrees) = 36.0 miles (rounded to one decimal place)

Next, we add up the North and West components separately to find the resultant displacement, which is the displacement from A to C.

N_A to C = N_A to B + N_B to C = 7.4 miles + 13.4 miles = 20.8 miles (rounded to one decimal place)

W_A to C = W_A to B + W_B to C = 34.7 miles + 36.0 miles = 70.7 miles (rounded to one decimal place)

Finally, we can calculate the magnitude and direction of the displacement from A to C using the North and West components.

Displacement magnitude (distance) = √(N_A to C^2 + W_A to C^2) = √(20.8^2 + 70.7^2) β‰ˆ 73.6 miles (rounded to one decimal place)

Displacement direction = arctan(W_A to C / N_A to C) = arctan(70.7 / 20.8) β‰ˆ 74.6 degrees North of West (rounded to one decimal place)

Therefore, the displacement from A to C is approximately 73.6 miles at 74.6 degrees North of West.