Question

A wildlife researcher is tracking a flock of geese. The geese fly 4.0 km due west, then turn toward the north by 50 degrees and fly another 4.5 km. What is the total distance covered by the geese?

1) 8.5 km
2) 9.0 km
3) 9.5 km
4) 10.0 km

Answer 1

The total distance covered by the geese is approximately 8.482 km.

Step-by-step explanation:

The total distance covered by the geese can be found using vector addition. The geese first fly 4.0 km due west and then turn toward the north by 50 degrees and fly another 4.5 km. To find the total distance, we need to find the magnitude of the resultant vector formed by adding the two displacement vectors together.

To do this, we can use the law of cosines: c^2 = a^2 + b^2 - 2ab cos(C), where c is the magnitude of the resultant vector and a and b are the magnitudes of the individual displacement vectors.

Using the law of cosines, we can calculate the magnitude of the resultant vector to be approximately 8.482 km. Therefore, the total distance covered by the geese is approximately 8.482 km.