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Unit 6 Polar Test Part 2 Page 2 No Calculator Name Sec _

Write the ~,QmR"'~liname of each polar equation graphed below.13. 14. 15.

13) _

16.

16) _

1,9.

J

19) _

14) 15) _

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17) _

20.

20) _

18.

18) ~-

21.

21 ) _

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Unit 6 Polar Test Part 2 Page 3 Calculator Name Sec _

22) Pick out the polar coordinate pairs that label thesame point. Several pairs may be possible.

22) _

a) (2,2;)e) (3,0)

b) (2, -;)

f) (-3,0)

c) (-3, JZ")

g) (-2, -;)d) (2, 7;)h) (-3, 2JZ")

23) (.3) ~j1)0 ')(-3Ji 3J23) Change -2-'2 to polar coordinates.

24) Change r = 2sinO-3cosO to rectangular form. 24) _

Identify the equation

25) Sketch a complete graph of r = 1+2cosO 26) Sketch the graph of r = 5cos( 50).

27) Give three additional polar coordinate pairs for the 27) _

point B( -4, ~). -21'[ ~ B ~21'[

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Unit 5 TX Assignment: Vector Apps Name Sec.

Please show all work - using vectors - and circle all answers. No work = no credit. All angles mustbe given to the nearest minute and all lengths to the nearest thousandths place.

1 airplane flies 200 km on course 110° from point A to point B. At point B the pilcurse 37°. The plane then fl'e'S' 0 km to point C. Find the magnitude of th,t,,~n,"t

fr m A to .

1~,..,..../44450773/04_pinkws_answers.pdf

rSThe velocity of the plane as

4) A ship leaves port at point A and sails 61.1 km on course 131°50' to point B. Then it sails 76.5 kmon course 36°30' to point C. Find the bearing of point C from point A.

5) An aircraft carrier is traveling on course 204°20' at 50 km per hour. An airplane leaves the carrierat point A and flies on course 328°20' to point C. The plane's displacement from A to C is 348 km.What course should the pilot set from point C in order to meet the carrier three hours after leaving it?

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be easie .

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break the ~elocities 0 x an y componentVx(ship)-cos(157)3 . =-32.4Vy (ship) = sin(157) 35.27 3.75

I Vx(current) cos(21~~;" = -6.71Vy (current) = sin(21~ 8 = -4.36

add the x's ana~y/-32.4 + (-6.71) = -39.11

13.75 + (-4.36) = 9.39

7) The angle between the heading and course of a ship is called the angle of drift.Find the angle of drift of an airplane with air speed 240 km/hr on heading 90° in a 65 km/hr wind inthe direction 0°. Find the ground speed of the airplane.

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11) A swimmer heads directly north across a river at 3 mph. The current of the river flows south at 2mph. What is the swimmer's actual speed in the river?

12) Two jeeps in the desert leave their starting points at noon. The first travels a course of 345° andaverages 23 mph. The second travels a course of 45° and averages 20 mph. How far apart are thetwo jeeps at 10 PM? What is the bearing from the first jeep to the second at this time?

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Unit 5 Test part 2 page 3

8. Given 17 = {S18}. (8 points)

a) What is the angle between the vector and the x- axis?

b) Write the vector in Polar Form.

9. Given 17 = {-4,2}, W = (6,-3). (10 points)

a) Find 217 - 3w.

b) Find 3w + 217 -w.

c) Find 2w' v.

a) Compute v+ w; v- w,and w- v.

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10. Let v= (1,6) and w= (5,-3). (16 points)

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Unit 5 Test part 2 page 2

s. Using satellite technology, a tracking station can determine the distance between two planes. If plane A is 176 milesfrom the tracking station and plane Bis 222 miles away and the angle between the two planes (from the tracking

station) is 38° 30'. How far apart are the two planes? (10 points)