Thread: vectors/displacement problem

A jogger travels a route that has two parts. The first is a displacement A of 2.90 km due south, and the second involves a displacement B that points due east.

(1) The resultant displacement A + B has a magnitude of 4.55 km. What is the magnitude of B?
What is the direction of A + B relative to due south?

(2) Suppose that A - B had a magnitude of 4.55 km. What then would be the magnitude of B and what is the direction of A - B relative to due south?
direction of A - B relative to due south

for part1:


B =

B =

B = 5.395 km

some how that answer is wrong, can someone explain?

When you draw the vectors, you form a right triangle:

Code:

    |\
    | \   
2.9 |  \   4.55 
    |   \
    |    \
    V----->
        B

By the Pythagorean theorem,

For part 2, A - B = A + (-B):

Code:

         /|
        / |
 A - B /  |  A
      /   |
     /    |
    *<----V
       B

The triangle doesn't change from part (1) and so the magnitudes should all be the same (but not the direction).

You can see that the direction of A - B is south and to the west by a few degrees. Use trigonometry to find the upper angle to determine the exact direction.

i did the Pythagorean theorem wrong. thanks!