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MA 167 Group Assignment 5

# MA 167 Group Assignment 5 - a Locate and compute the...

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MA 167 – Group Work - 5 Group Name _________________________ Members ________________________ ________________________ ________________________ ________________________ Assignment due Friday 10/9/09 Derivatives Textbook problems: Section 3.1 (page 155) #47 – 51, 57 Section 3.2 (pages 167 – 168) #41, 44 Trigonometry Textbook problems: Section 3.4 (page 188) #55 – 57 1. a . Tafu attaches a weight to a spring, as shown, and gives it a tug. He models the height of the weight above his desk with the formula , ) 1 ( 3 sin 4 7 - + = t y π where y is in inches and t is in seconds. Give a formula for the velocity of the weight at time t . b. During the first 9 seconds, when is the velocity of the weight equal to 3 2 - inches per second?

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Parametric Equations 2. An object is moving around an ellipse according to the parametric equations ) 5 sin( ) ( ) 5 cos( 2 ) ( t t y t t x = = where t has units of seconds and the coordinate axes have units of feet. The location of the object at time t will be )) ( ), ( ( ) ( t y t x t P = and the graph of this motion is given below:
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Unformatted text preview: a. Locate and compute the coordinates of P (0), P (0.5), and P (1) in the picture. b. Compute the horizontal velocity ) ( t x ′ and vertical velocity ) ( t y ′ . What are the maximum (minimum) vertical and horizontal velocities? c. During the first trip of the object around the ellipse, find where the object is located when it has vertical velocity 3 ft/sec. d. During the first trip of the object around the ellipse, how much of the time will the horizontal velocity exceed 8 ft/sec? e. Plot the point )) 1 ( ) 1 ( ), 1 ( ) 1 ( ( ) 1 ( y y x x Q ′ + ′ + = and find the equation of a line through the points P (1) and Q (1). Draw this line in the picture. What can you say about this line? f. Plot the point )) 5 . ( ) 5 . ( ), 5 . ( ) 5 . ( ( ) 5 . ( y y x x Q ′ + ′ + = and find the equation of a line through the points P (0.5) and Q (0.5). Draw this line in the picture. What can you say about this line?...
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MA 167 Group Assignment 5 - a Locate and compute the...

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