Question

1. renee has walked in a straight line, 25° west of north, for 1200 meters. how far south and east should she walk to return to her original location?

508 m south, 1088 m east
600 m south, 600 m east
1088 m south, 508 m east
1200 m south, 25 m east

Explanation:

Step1: Find the south - ward component

The south - ward component \(y\) of the displacement. We know that if the angle with the north is \(\theta = 25^{\circ}\) and the magnitude of the displacement \(d=1200\) m. Using the sine function \(y = d\sin\theta\).
\(y=1200\times\sin(25^{\circ})\)
Since \(\sin(25^{\circ})\approx0.4226\), then \(y = 1200\times0.4226=507.12\approx508\) m.

Step2: Find the east - ward component

The east - ward component \(x\) of the displacement. Using the cosine function \(x = d\cos(90^{\circ}-\theta)\) (because the angle with the west - east line is \(90^{\circ}-\theta\)). Also, we can use the co - function identity \(\cos(90^{\circ}-\alpha)=\sin\alpha\) and another approach: if we consider the right - triangle formed by the displacement vector, the south - ward and east - ward components. The angle with the west - east line is \(25^{\circ}\), and using \(x = d\cos(25^{\circ})\)
Since \(\cos(25^{\circ})\approx0.9063\), then \(x = 1200\times0.9063 = 1087.56\approx1088\) m

Answer:

1088 m south, 508 m east (the third option)