1- The polar coordinates of a certain point are ( r = 3.25 cm, = 185°). (a) Find

Question

1- The polar coordinates of a certain point are (r = 3.25 cm, =  185°).

(a) Find its Cartesian coordinates x and y.

(b) Find the polar coordinates of the points with Cartesian coordinates (x, y).

(c) Find the polar coordinates of the points with Cartesian coordinates (2x, 2y).

(d) Find the polar coordinates of the points with Cartesian coordinates (3x, 3y).

2- A plane flies from base camp to Lake A, 240 km away in the direction 20.0° north of east. After dropping off supplies it flies to Lake B, which is 240 km at 30.0° west of north from Lake A. Graphically determine the distance and direction from Lake B to the base camp.

3- Obtain expressions in component form for the position vectors having the following polar coordinates.

Explanation / Answer

1. A) x = rcos@ = 3.25 cos185 = - 3.24 cm

y = rsin@ = 3.25sin185 = -0.283 cm

B) r = sqrt(x^2 + y^2) = 3.25 cm

@ = 180 - tan^-1(0.283/3.24) = 175 deg

C) r = ((2x)^2 + (2y)^2) = ((2x3.24)^2 + (2x0.283)^2) = 6.50 cm

@ = 185 deg

D) r = ((3x)^2 + (3y)^2) = ((3x3.24)^2 + (3x0.283)^2) = 9.76 cm

@ = 355 deg

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