Oasis B is a distance d = 9 km east of oasis A, along the x axis shown in the Figure. A confused camel, intending to walk directly from A to B instead walks a distance W1 = 20 km west of due south by angle θ1 = 15.0°. It then walks a distance W2 = 32 km due north. If it is to then walk directly to B, (a) how far (in km) and (b) in what direction should it walk (relative to the positive direction of the x axis)?

Question

Oasis B is a distance d = 9 km east of oasis A, along the x axis shown in the Figure. A confused camel, intending to walk directly from A to B instead walks a distance W1 = 20 km west of due south by angle θ1 = 15.0°. It then walks a distance W2 = 32 km due north. If it is to then walk directly to B, (a) how far (in km) and (b) in what direction should it walk (relative to the positive direction of the x axis)?

i found how far it was, but how do you find in what direction it should walk? i set up a tan of theta= oppisite/adjacent, but this didn't give me the right answer

Answer 1

sketch the diagram, that will give you a good idea of the quadrant the angle is in, you cant trust your calculator, as it only gives principle angles.

Answer 2

To find the direction in which the camel should walk, we need to determine the angle it needs to move relative to the positive direction of the x-axis.

Let's break down the problem step by step:

1. Find the horizontal distance the camel walks to the east (W1 component):
Since the camel walks 20 km west of due south, we can find the eastward component using trigonometry.
W1 = W1 component = W1 * cos(θ1) = 20 km * cos(15°) = 19.313 km (rounded to three decimal places)

2. Find the vertical distance the camel walks to the north (W2 component):
The camel walks 32 km due north, so the vertical distance is already aligned with the positive y-axis.
W2 = W2 component = 32 km

3. Find the total distance the camel needs to travel to reach oasis B (R):
R = √(W1^2 + W2^2) = √(19.313^2 + 32^2) ≈ 37.501 km (rounded to three decimal places)

Now, to find the direction the camel should walk:

4. Calculate the direction angle (θ) relative to the positive direction of the x-axis:
θ = tan^(-1)(W1/W2) = tan^(-1)(19.313/32) = 31.768° (rounded to three decimal places)

The answer to part (a) is the total distance: 37.501 km.
The answer to part (b) is the direction angle: 31.768° (relative to the positive direction of the x-axis).

sketch the diagram, that will give you a good idea of the quadrant the angle is in, you cant trust your calculator, as it only gives principle angles.

21

To find the direction in which the camel should walk, we need to determine the angle it needs to move relative to the positive direction of the x-axis.