Aperson walks37.7◦ northofeast for 3.54km. Another person walks due north, then due east to arrive at the same location. How far due north would this person walk?
To determine the distance the second person would walk due north, we can use vector addition.
Let's designate the following vectors:
- Vector A: The displacement of the first person who walks 37.7° north of east for 3.54 km.
- Vector B: The displacement of the second person who walks due north, and then due east.
Since the first person walks 37.7° north of east, we know that the horizontal component of their displacement (i.e., east) is given by:
Ax = 3.54 km * cos(37.7°)
To determine the vertical component of their displacement (i.e., north), we can use:
Ay = 3.54 km * sin(37.7°)
Now, for the second person, we know that their total displacement must be equal to Vector A. Therefore, the vertical component of their displacement (i.e., north) would be equal to Ay.
So, the distance the second person would walk due north is approximately 2.366 km (Ay = 3.54 km * sin(37.7°)).