3. Tarzan Problem Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across the riverbank, going alternatively over land and water. Jane decides to model mathematically his motion and starts her stopwatch. Let t be the number of seconds the stopwatch reads and y be the number of meters Tarzan is from the river bank. Assume that y varies sinusodially with t, and that y is positive when Tarzan is over water and negative whén he is over land. Jane finds that when t= 2. Tarzan is at one end of his swing, where y-23. She finds that when t-5 he reaches the other end of his swing and y 17. a. Sketch a graph of this sinusoid. b. Write an equation expressing Tarzan's distance from the riverbank in terms of t. c. Predict y when 1=2.8 1=6.3 t-15 i. il. d. Where was Tarzan when Jane started her stopwatch? e. Find the least positive value oft for which Iarzan is directly over the river bank (Le. y 0)
3. Tarzan Problem Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across the riverbank, going alternatively over land and water. Jane decides to model mathematically his motion and starts her stopwatch. Let t be the number of seconds the stopwatch reads and y be the number of meters Tarzan is from the river bank. Assume that y varies sinusodially with t, and that y is positive when Tarzan is over water and negative whén he is over land. Jane finds that when t= 2. Tarzan is at one end of his swing, where y-23. She finds that when t-5 he reaches the other end of his swing and y 17. a. Sketch a graph of this sinusoid. b. Write an equation expressing Tarzan's distance from the riverbank in terms of t. c. Predict y when 1=2.8 1=6.3 t-15 i. il. d. Where was Tarzan when Jane started her stopwatch? e. Find the least positive value oft for which Iarzan is directly over the river bank (Le. y 0)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:3. Tarzan Problem
Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth
across the riverbank, going alternatively over land and water. Jane decides to model mathematically his
motion and starts her stopwatch. Let t be the number of seconds the stopwatch reads and y be the
number of meters Tarzan is from the river bank. Assume that y varies sinusodially with t, and that y is positive
when Tarzan is over water and negative when he is over land.
Jane finds that when t = 2. Tarzan is at one end of his swing, where y=-23. She finds that whent=5 he
reaches the other end of his swing and y = 17.
a. Sketch a graph of this sinusoid.
b. Write an equation expressing Tarzan's distance from the riverbank in terms of t.
c. Predict y when
i.
i.
i.
d. Where was Tarzan when Jane started her stopwatch?
e. Find the least positive value oft for which Tarzan is directly over the river bank (i.e. y- 0)
1 = 2.8
1=6.3
t= 15
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