Question

Find the resultant displacement of a bear searching for berries on the mountain. The bear heads 55.0º north of west for 15.0 m; then it turns and heads to the west for another 7.00 m.

Answer 1

north component: y = 15.0m * sin55.0º = 12.3 m west component: x = 15.0m * cos55.0º + 7.00m = 15.6 m so his heading, measured from West, is Θ = arctan(y/x) = arctan0.787 = 38.2º N of West and measured from North is φ = arctan(x/y) = arctan(1.27) = 51.8º W of North