Answer:
a) The fly is 2.24 m from the origin.
b) In polar coordinates, the position of the fly is (2.24 m, 26.7°).
Explanation:
Hi there!
The position vector of the fly is r = (2.00, 1.00)m. The distance from that point to the origin is the magnitude of the vector "r" (see figure).
a) Notice in the attached figure that the distance from the origin to the point where the fly is located is the hypotenuse of the triangle formed by r, the x-component of r (2.00 m) and the y-component ( 1.00 m). Then:
r² = (2.00 m)² + (1.00 m)²
r² = 5.00 m²
r = 2.24 m
The fly is 2.24 m from the origin.
b) To find the angle θ (see figure) we can use trigonometry:
cos θ = adjacent / hypotenuse
cos θ = 2.00 m / √5 m
θ = 26.7°
The same will be obtained if we use sin θ:
sin θ = opposite / hypotenuse
sin θ = 1.00 m / √5 m
θ = 26.7°
In polar coordinates, the position of the fly is (2.24 m, 26.7°).
