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Warm Up. 2) Imagine you are piloting a small plane at an altitude of 15,000 feet and preparing to land. Once you begin your descent to the runway, your altitude changes at a rate of-25 feet/sec. Your horizontal speed is 180 ft /sec.

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Warm up

Warm Up

2) Imagine you are piloting a small plane at an altitude of

15,000 feet and preparing to land. Once you begin your

descent to the runway, your altitude changes at a rate

of-25 feet/sec. Your horizontal speed is 180 ft /sec.

Write parametric equations to model the descent of

your plane.

The function y = f (x) is defined parametrically by

x(t) = 1 + 3t, y(t) = 2t2 + 5. Write y as a function

of x and sketch the graph of the function f.

1) Determine whether or not (104, -200) is a point

on the graph of x = 4 + t, y = 100 - 3t.


Warm up

Warm Up Answers

1) Substitute (104, -200) in each equation and solve.104 = 4 + t, so t = 100-200 = 100 - 3t, t = 100 Since the t values are the same, the point is on the graph. 2) x(t) = 180t y(t) = 15000 - 25t


Testlet review

Testlet Review

Parametric Equations & Vectors


Non calculator

Non-Calculator

  • Eliminate the parameter to write y as a function of x.

    x = 4T – 1, y = -8T + 2

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


Non calculator1

Non-Calculator

  • Solve for r and s, so that the statement is true.


Non calculator2

Non-Calculator

b) | v |

d) unit vector in the same direction as w


Non calculator3

NON-Calculator

1) Find the component form of a vector with magnitude 4 and direction 300.

2) Find the value of k so that the vectors are

  • orthogonal,

  • parallel


Non calculator4

Non-Calculator

  • Find u●vif | 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


Non calculator5

NON-Calculator

  • Identify whether the vectors are orthogonal, parallel or neither.

    • u = 3i – 2j , v = -4i +6

    • u = i – 2j , v = -2i +4j

    • u = – 2j , v = -4i

    • u = ½ i – ¾ j , v = 18i + 12


Calculator active neutral

Calculator Active/Neutral

  • There 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 minutes 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 minutes she has been flying.


Calculator active

Calculator Active


Calculator

Calculator

  • Find the direction of the vector (Remember: No negative angles)

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


Calculator active neutral1

Calculator Active/Neutral

  • Write a pair of parametric equations that define the inverse relation for the given parametric equations x = t3- 2, y = 2t

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


Calculator active neutral2

Calculator Active/Neutral

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.

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

  • Sketch a graph to represent the path of the geese over a 5 hour period.

  • Find the speed of the geese in mm/min.

  • Write a linear function to represent the path of the geese.

  • 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 active1

Calculator Active

A plane is flying on a bearing N10W at 460mph. The wind is blowing in the direction S25E at 30mph. Express the actual velocity of the plane as a vector. Determine the actual speed and direction of the plane.


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