Answer
4.25m
Work Step by Step
vector a is moving towards the east which is on the positive x-axis
and vector b is at an angle between the north and west direction which is in between the positive y and negative x axis.
vector a = 5m $i$
vector b = (4sin(35) $i$ + 4cos(35) $j$ )m = ( -2.29 $i$ + 3.28 $j$ )m
vector a + vector b = (5 $i$ - 2.29 $i$ + 3.28 $j$ )m = (2.71 $i$ + 3.28 $j$ )m
Magnitude of vector a + vector b = $\sqrt (2.71^2 + 3.28^2)$ = 4.25m
Therefore the length of vector a + vector b is 4.25m
