Given that a wildlife researcher is tracking a flock of geese and that the geese fly 3.5 km due west, then turn toward the north by 50° and fly another 4.5 km, we are to determine:
(A) How far west are they of their initial position?
To determine how far west they are of their initial position, we need to find the distance traveled in the westward direction. This can be found by projecting the 4.5 km flight on the line of due west. Using trigonometry, we can find that this distance is:3.5 km + 4.5 km cos 50° ≈ 6.22 km
Therefore, they are approximately 6.22 km west of their initial position.
(B) What is the magnitude of their displacement?
To determine the magnitude of their displacement, we can use the Pythagorean theorem. We have: Displacement = √(Westward distance)² + (Northward distance)²= √(6.22 km)² + (4.5 km sin 50°)²≈ 7.91 km
Therefore, the magnitude of their displacement is approximately 7.91 km.
Initial Position : The point at which a body is released or initiated is called the initial position. The final position is the point at which a body stops or travels a certain distance from one point to another.