Question

1. a hiker walks 17.2 m, e and 9.87 m, n. what is the direction of his resultant displacement?

29.9 (n/e)

Explanation:

Step1: Identify the components

The hiker's displacement has an eastward component (\(x = 17.2\space m\)) and a northward component (\(y = 9.87\space m\)). To find the direction (the angle \(\theta\) from the east direction towards the north), we use the tangent function.

Step2: Use the tangent formula

The tangent of the angle \(\theta\) is given by \(\tan\theta=\frac{y}{x}\), where \(y\) is the northward displacement and \(x\) is the eastward displacement.
Substitute \(y = 9.87\space m\) and \(x = 17.2\space m\) into the formula:
\(\tan\theta=\frac{9.87}{17.2}\)

Step3: Calculate the angle

First, calculate \(\frac{9.87}{17.2}\approx0.5738\)
Then, find the arctangent (inverse tangent) of \(0.5738\):
\(\theta=\arctan(0.5738)\approx29.9^\circ\)
This angle is measured from the east axis towards the north axis, so the direction is \(29.9^\circ\) North of East.

Answer:

The direction is \(29.9^\circ\) North of East (or \(29.9^\circ\) \(\frac{N}{E}\))