Warm Up May 13th In your new job for the Gearing, Engineering, Evaluation, and

Kinematics team, aka the GEEK team, you must analyze movements of battle robots that will be competing next month. Your robot is placed in a 100-by-100-ft arena. Its initial position is 2.5 feet from the south wall of the arena and 5 feet from the west wall. After starting the robot with your remote, it moved for 1 second. Its new position is 14.5 feet from the south wall and 10 feet from the west wall. Another member of the GEEK team started her robot 75 feet from the west wall of the arena just against the south wall. After 1 second, her robot was 62 feet from the west wall and 16 feet from the south wall. Answer the following questions. Assume that both robots continue at the same speed and on the same path.

a. Sketch the paths of the robots. Write the linear equations to represent their paths.

b. Where do their paths cross?c. Find the speed in feet per second that both robots are moving.d. Write parametric equations for both robots.e. How long does it take each robot to get to the point where their

paths cross?

Homework Check/Questions?1. a) <-136.868, 336.042>

b) 362.846 mphc) 112.161°

2. a) <52.517, -528.187>b) 530.719 mphc) 275.678°

3. Plane: <-452.995, 20.603>Speed: 433.485 mphDirection: 177.276°

4. Plane: <13.892, 758.785>Speed: 758.912 mphDirection: 88.951°

Book Page 519 – 521 Evens

Check6. -4434. Neither36. Orthogonal

Intro to Polar Coordinates

Plotting Points

Differences: Polar vs. RectangularPOLAR RECTANGULAR• (0, 0) is called the pole• Coordinates are in form (r, θ)

• (0, 0) is called the origin• Coordinates are in form (x, y)

Plot Given Polar Coordinates

• Locate the following

2,4

A

33,

2C

24,

3B

51,

4D

Plot Given Polar Coordinates

• Locate the following

2,3

2,3

2

5,3

2

3,3

You Try!• Locate the following

4

3,3 .2

3

2,4 .3

6,5 .1

Find Polar Coordinates• What are the coordinates for the given points?

• B• A

• C

• D

• A =

• B =

• C =

• D =

Test Review Trashketball

Parametric Equations & Vectors

Non-Calculator1. Eliminate the parameter to write y

as a function of x. x = 4T – 1, y = -8T + 2

2. Given the initial point (3, 2) and the terminal point (3, -5) of a vector, write the component form.

Non-Calculator1) Find the component form of a vector

with magnitude 4 and direction 300.

2) Find the value of k so that the vectors are a) orthogonalb) parallel

and 4,k 10,6

Calculator ActiveThere is a new superhero and her name is

SuperSigma. Only she is not so super! SuperSigma is super drunk (on coca-cola, of course) and she’s flying in circles. The radius of her flight path is 5 feet and it takes her 30 seconds to stumble (fly) around the circle once. Her flight path has been

graphed so that the center of the circle is (5, 0). If she starts her flight at (0, 0) and flies in a counter-clockwise direction, write parametric equations to

model SuperSigma’s location in terms of the number of seconds she has been flying.

Non-Calculator• Identify whether the vectors are

orthogonal, parallel or neither.

a) u = 3i – 2j , v = -4i + 6

b) u = i – 2j , v = -2i + 4j

c) u = – 2j , v = -4i

d) u = ½ i – ¾ j , v = 18i + 12j

Calculator Active1. At a softball throwing contest, you have to throw

the ball at least 100 feet in order to make it into the semi-final round. You throw a softball with an initial velocity of 60 feet per second and a 50° angle with the ground from an initial height of 5.5 feet. Did you make it into the semi-final round?

If not, adjust the angle in order to make it into the semi-finals.

If so, you move on to the final round where you have to throw the softball at least 150 feet, so adjust the initial velocity to make it into the final round.

Non-Calculator4,3 , 2, 4 ,and 2, 3 u v w

)a 2u3w

) ( )c u v w

b) | v |

d) unit vector in the same direction as w

Calculator Active Your neighbor is studying the migration of a certain

gaggle of geese. Because of your awesome math skills, he has asked for your help. You have laid out a topological map to indicate the movement of the geese over time with your house corresponding to the point (0,0) on the grid. The geese start their migration at the point (420mm, 30mm) on the grid and move in a linear path to a location 0.8 mm west and 0.2 mm north every minute.

1. Write parametric equations to represent the movement of the geese.

2. There is a small pond located on the grid at the point (230, 75). Will the geese fly over the pond? If yes, when?

Calculator Active As your neighbor observes the gaggle of geese,

a flock of seagulls appear to be headed straight toward the gaggle.The geese’s path can be modeled by

x = 420 – 0.8t and y = 30 + 0.2tThe flock’s path can be modeled by

x = 70 + 0.9t and y = 10 + 0.4tDo the birds “collide”? If so, when? If not, what is the minimum distance between them?

Calculator Active1. Find the direction of the vector

2. Write the component form of a vector with magnitude 8 and direction 73.

2, 6

Non-Calculator1) Find u●v if | u | = 4 and | v | = 6

and the angle between u and v is 150.

2) Find the values of t so that the angle between the vectors is obtuse

3,7 and ,6t

Calculator ActiveA plane is flying on a bearing N10W at 460mph. The wind is blowing in the direction S25E at 30mph. Express the actual velocity of the plane as a vector. Determine the actual speed and direction of the plane.

Calculator ActiveA dolphin is performing at Sea World and leaps out of the water at an initial speed of 32 feet per second at an angle of 48° with the water.

a) How far does the dolphin jump?

b) What is the maximum height of the jump?

Calculator Active1. Eliminate the parameter to write y as a

function of x. x = t3- 2, y = 2t

2. A boat leaves a port and sails 16 mph at the bearing S 20E. Write a vector to represent the velocity of the boat.

Calculator ActiveA Ferris wheel with a radius of 47 feet turns

clockwise at the rate of one revolution every 80 seconds. The lowest point of the Ferris wheel is 15 feet above ground level

at the point (0, 15) on a rectangular coordinate system. Write the parametric equations for the position of a person on the Ferris wheel as a function of time (in seconds) if the Ferris wheel starts (t = 0) with the person at the point (47, 62). Find the height of a person after 45 seconds.

Non-CalculatorSolve for r and s, so that the statement is true.

) , 3, 2 5,7 a r s

) 3 , 2 2 5, 2,10 b r s