Vector Sample Problem Answers

1. Walking on a sidewalk, you first travel 500m west, then 200m south, and finally 100m east. What is your resultant displacement?

447.214m at 206.565°

First, since east and west represent horizontal components, we can add them together. Then we perform our normal vector adding calculations using the numbers.

sqrt((-400m)^2+(-200m)^2)
447.214m
tan^-1(-200m/-400m)
26.565°

Since, both values are negative, we know the answer must be in the third quadrant, therefore we have to add 180° to it giving us a final answer of 206.565°.

2. If A is 2m at 45° and B is 2m at 330°, use i, j, k notation to find:
a. A + B
b. 2A + B
c. A - B
d. B - A

a. 3.146mi + 0.414mj
b. 6.292mi + 0.414mj
c. -0.318mi + 2.414mj
d. 0.318mi + -2.414mj

First, we convert the vectors into their horizontal and vertical components, then we perform the desired functions.

2m cos 45° = 1.414mi
2m sin 45° = 1.414mj
2m cos 330° = 1.732mi
2m cos 330° = -1.0mj

a. (1.414mi + 1.414mj) + (1.732mi - 1.0mj)
3.146mi + 0.414mj
b. 2 * (1.414mi + 1.414mj) + (1.732mi - 1.0mj)
6.292mi + 0.414mj
c. (1.414mi + 1.414mj) - (1.732mi - 1.0mj)
-0.318mi + 2.414mj
d. (1.732mi - 1.0mj) - (1.414mi + 1.414mj)
0.318mi + -2.414mj