To solve this problem, we need to find how far south the robin is from its starting point after flying 21 km at a bearing of 039° and then 36 km due south.

Step 1: Resolve the components of the 21 km leg

• The bearing of 039° means the robin flies 39° east of due north. We can break this 21 km flight into northward and eastward components using trigonometric functions: $\text{Northward component} = 21 \cos(39°)$ $\text{Eastward component} = 21 \sin(39°)$

Step 2: Calculate the net southward distance

• After traveling northward for the first leg, the robin then flies 36 km south. The net southward displacement from the starting point is: $\text{Net southward displacement} = 36 - 21 \cos(39°)$

Let's calculate these values.

Calculations:

1. $21 \cos(39°) \approx 21 \times 0.7771 \approx 16.32 \text{ km}$
2. Net southward displacement: $36 - 16.32 = 19.68 \text{ km}$

Thus, the robin lands approximately 19.7 km south of its starting point.

Would you like to see more details or have any questions?

Related Questions:

1. How would the calculation change if the second leg was not directly south?
2. What is the total distance the robin traveled?
3. How would you find the final distance from the starting point to the finish?
4. How would you determine the eastward displacement?
5. Can you solve this using vectors?

Tip:

Using trigonometry to resolve vectors into components simplifies solving problems with bearings and angles.