Afly lands on one wall of a room. the lower-left corner of the wall is selected as the origin of a two-dimensional car- tesian coordinate system. if the fly is located at the point having coordinates (2.00, 1.00) m, (a) how far is it from the origin? (b) what is its location in polar coordinates?

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°).

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