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16. Consider a trajectory along a piece of the IT astroid r(t) = (cos't,sin's), for 0515 2 where the components of r have units of meters and / has units of time (Figure 1). What is the speed along the path? Where along the path is the speed greatest? Least?

16. Consider a trajectory along a piece of the IT astroid r(t) = (cos't,sin's), for 0515 2 where the components of r have units of meters and / has units of time (Figure 1). What is the speed along the path? Where along the path is the speed greatest? Least?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 40E
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16. Consider a trajectory along a piece of the astroid r(t) = (cos't, sin³t), for 05152 where the components of r have units of meters and has units of time (Figure 1). What is the speed along the path? Where along the path is the speed greatest? Least? 17. Suppose you want to design a trajectory along the segment of the astroid in Step 16 with a constant speed of Vo. Carry out the procedure outlined above by assuming the trajectory has the form r(t) = (cos' u(t), sin' u(t)), for OSIST. Show that the required function u may be expressed in either of the following two equivalent forms: 11-2061 3 8.5 u(t)= cos ¹. -0.5 sin-2Vot 3 18. What value of T should be used so the trajectory in Step 17 starts at (1, 0) and ends at (0, 1)? 8.5 Figure 1
Transcribed Image Text:16. Consider a trajectory along a piece of the astroid r(t) = (cos't, sin³t), for 05152 where the components of r have units of meters and has units of time (Figure 1). What is the speed along the path? Where along the path is the speed greatest? Least? 17. Suppose you want to design a trajectory along the segment of the astroid in Step 16 with a constant speed of Vo. Carry out the procedure outlined above by assuming the trajectory has the form r(t) = (cos' u(t), sin' u(t)), for OSIST. Show that the required function u may be expressed in either of the following two equivalent forms: 11-2061 3 8.5 u(t)= cos ¹. -0.5 sin-2Vot 3 18. What value of T should be used so the trajectory in Step 17 starts at (1, 0) and ends at (0, 1)? 8.5 Figure 1
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