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4.1 pt 2 (1) - 234 4 Vector-Valued Funetions In Exercises...

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Unformatted text preview: 234 4. Vector-Valued Funetions In Exercises 5—8, let c1[t) = eti+( sin t)i+t3k and Cam 2 e"*i+( cos t)i—2t3 Find each of the stated derivatives in two different ways to verify the rules ' the box preceding Example 1. 5. gm) +C2ltll 6. filers) «am 7. git—[cam x can] :1 s. a{c.(l) « [2mm + c1011} 9. If rm = fiti + 3t21+t3k (see Exercise 1), what force acts on a particle mass or moving along 1' at t = 0? 10. A particle of mass of 1 gram follows the path r01) = sin 3ti + cos 313‘ 2t3/2k (see Exercise 2), with units in seconds and centimeters. What f acts on it at t = 0? (Give the units in your answer.) 11. A body of mass 2 kilograms moves in a circular path on a circle of radius meters, making one revolution every 5 seconds. Find the centripetal lo.- acting on the body. 12. Find the centripetal force acting on a body of mass 4 kilograms, moi-'- on a circle of radius 10 meters with a frequency of two revolutions second. 13. Show that if the acceleration of an object is always perpendicular to " velocity, then the speed of the object is constant. (Hint: See Example 1 14. Show that, at a local maximum or minimum of llr[t)ll, r’ (t) is perpen ' ular to r(t). 15. A satellite is in a circular orbit 500 miles above the surface of the Ea.- “What is the period of the orbit? (You may take the radius of the Earth be 4000 miles.) 16. What is the gravitational acceleration on the satellite in Exercise 15? T’ centripetal acceleration? ...
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