Oasis B is a distance d = 8.0 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 = 21 km west of due south by angle θ1 = 15.0°. It then walks a distance W2 = 30 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 within the range (-180°, 180°])?

d = 21km@255o + 30km@90o + 8km@0o.

X = hor. = 21*cos255 + 8 = 2.56 km.
Y = Ver. = 21*sin255 + 30*sin90=9.72 km.

a. d^2=X^2 + Y^2=(2.56)^2 + (9.72)^2=101
d = 10.1 km.

tanA = Y/X = 9.72/2.56 = 3.79688
A = 75.2o,CCW = 75.2o North of East = The Direction.

34

this one up top is the wrong way of doing this problem

To find the distance and direction the camel should walk from its current position to reach B, we can break the distance into two components, one along the x-axis and the other along the y-axis.

First, let's find the x-component of the distance the camel needs to travel. The camel has already walked a distance of W1 = 21 km west of due south, which forms a right triangle with the x-axis. We can use trigonometry to find the x-component of W1.

Given the angle θ1 = 15.0° and the magnitude of W1 = 21 km, we can use the cosine function to find the x-component:

x-component of W1 = W1 * cos(θ1)

Plugging in the values:

x-component of W1 = 21 km * cos(15.0°)

Calculating this expression gives us the x-component of W1.

Next, let's find the y-component of the distance the camel needs to travel. The camel has walked a distance of W2 = 30 km due north, which is the y-component of the total distance.

Now we have the x-component and y-component of the distance the camel needs to travel. We can find the total distance by using the Pythagorean theorem:

Total distance = sqrt((x-component of W1)^2 + (y-component of W2)^2)

This will give us the total distance the camel needs to travel to reach B.

To find the direction the camel should walk, we can use the inverse tangent function. The direction will be the angle formed between the positive x-axis and the line connecting the camel's current position to the target position B.

Direction = atan((y-component of W2) / (x-component of W1))

This will give us the direction in radians. To convert it to degrees, multiply by 180/π.

To summarize:

(a) The total distance the camel should walk is found using the Pythagorean theorem:
Total distance = sqrt((x-component of W1)^2 + (y-component of W2)^2)

(b) The direction the camel should walk is found using the inverse tangent function:
Direction = atan((y-component of W2) / (x-component of W1))

Remember to convert the direction from radians to degrees.