Question

1. cory is looking for a good campsite. from where he parked, he walks for 144 meters 29° south of west. he then turns directly north, and walks for another 215 meters, where he finds a campsite. when he is giving directions to his friends, which of the following sets of instructions will bring them to the correct location? walk 145 meters west, then go 126 meters north walk 285 meters east, then go 125 meters north walk 285 meters north, then go 125 meters east walk 145 meters north, then go 126 meters west

Explanation:

Step1: Decompose the first - walk vector

The first walk is \(144\) meters \(29^{\circ}\) south of west.
The west - component \(x_1 = 144\cos29^{\circ}\approx144\times0.875 = 126\) meters (west direction).
The south - component \(y_1=144\sin29^{\circ}\approx144\times0.485 = 70\) meters (south direction).

Step2: Analyze the second - walk vector

The second walk is \(215\) meters north. So the net north - component \(y = 215 - 70=145\) meters (north direction). And the net west - component \(x = 126\) meters (west direction).

Answer:

Walk 145 meters north, then go 126 meters west.