Question

The colored lines in the figure represent paths taken by different people walking around in a city. Assume that each city block is 110 m long.

Calculate the magnitude and direction of the displacement vector of path D. I cannot get the last part for direction

Answer 1

Answer: 592.37m

Step-by-step explanation:

Person D is the blue line.

The total displacement is equal to the difference between the final position and the initial position, if the initial position is (0,0) we have that he first goes down two blocks, then right 6 blocks. then up 4 blocks, then left 1 block.

Now i will considerate that the positive x-axis is to the right and the positive y-axis is upwards.

Then the new position will be, if B is a block:

P =(6*B - 1*B, -2*B + 4*B) = (5*B, 2*B)

And we know that B = 110m

P = (550m, 220m)

Now, then the displacement will be equal to the magnitude of our vector, (because the difference between P and the initial position is equal to P, as the initial position is (0,0)) this is:

P = √(550^2 + 220^2) = 592.37m