Question

Suppose you walk 11 m in a direction exactly 24' south of west then you walk 21 m in a direction exactly 39

how far are you, in meters, from your starting point?

Answer 1

To find the distance from the starting point, break down the two legs of the walk into their horizontal and vertical components. Add up the components separately and use the Pythagorean theorem to find the magnitude of the resultant displacement. The compass direction can be found using trigonometry.

Step-by-step explanation:

To find the distance from the starting point, we need to obtain the resultant displacement. Let's start by breaking down the two legs of the walk into their horizontal and vertical components.

First leg: 11 m in a direction 24' south of west. The horizontal component is 11 * sin(24') and the vertical component is 11 * cos(24').

Second leg: 21 m in a direction 39° south of west. The horizontal component is 21 * sin(39°) and the vertical component is 21 * cos(39°).

Next, we add up the horizontal and vertical components separately for both legs. Finally, we use the Pythagorean theorem to find the magnitude of the resultant displacement. The magnitude is the distance from the starting point, and the direction can be found using trigonometry.

Calculating the values, we find that the distance from the starting point is approximately 28.2 m. The compass direction of the line connecting the starting point to the final position is approximately 4.6° south of west.