1.)The polar coordinates of a point are r = 5.60 m and = 200°. What are the Cart

Question

1.)The polar coordinates of a point are r = 5.60 m and = 200°. What are the Cartesian coordinates of this point?
x =  m
y =  m

2.)If the rectangular coordinates of a point are given by (9, y), and its polar coordinates are (r, 19°), determine the value of y and r.

3.)Two points in the xy plane have Cartesian coordinates (5.00, 5.50) m and (4.00, 4.00) m.

(a) Determine the distance between these points.
m

(b) Determine their polar coordinates.

4.)

Two points in a plane have polar coordinates (2.80 m, 40.0°) and (4.50 m, 110.0°).

(a) Determine the Cartesian coordinates of these points.
(2.80 m, 40.0°)
x =  m
y =  m
(4.50 m, 110.0°)
x =  m
y =  m

(b) Determine the distance between them.
m

6.)A roller-coaster car moves 216 ft horizontally and then rises 115 ft at an angle of 33.0° above the horizontal. It next travels 115 ft at an angle of 46.0° downward (below the horizontal). What is its displacement from its starting point? (Assume the initial horizontal motion of the car to be along the +x axis.)

7.)A plane flies from base camp to Lake A, 310 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.

8.)A vector has an x component of -23.0 units and a y component of 42.2 units. Find the magnitude and direction of this vector.

9.)A person walks 30.0° north of east for 3.02 km. How far would she have to walk due north and due east to arrive at the same location?

10.)Use the component method to add the vectors

and

shown in the figure. Both vectors have magnitudes of 3.45 m and vector

makes an angle of

= 24.5°

with the x axis. Express the resultant

in unit-vector notation.

(d) Calculate

Explanation / Answer

1) x = rcostheta = 5.6cos200 = -5.26 m

y = r sin200 = -1.92 m

2) x = 9 = rcos19

r = 9/ cos19 = 9.52 m

y = 9.52sin19 = 3.09 m

3) a) d = sqrt(x2-x1)^2+(y2-y1)^2

d = 13.08 m

b) r = sqrt(x^2+y^2) = 7.43 m

theta = 312.3 degrees

r = sqrt(4^2+4^2) = 5.65 m

theta = tan^-1(y/x) = 135 degrees

4) x = 2.8cos40 = 2.14 m

y = 2.8sin40 = 1.79 m

x = 4.5cos110 = -1.54 m

y = 4.5sin110 = 4.2 m

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