hw9-sol - Page 1 Assignment 9 100 points total Section 17.2...

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Unformatted text preview: Page 1 Assignment 9 100 points total Section 17.2 Problem 2 : the velocity vector is given by: = ? ?? ¡ 2 + 3 ?¢݅ + ? ?? ¡ 4 + ?¢݆ + ? ?? ¡ 1 − ?¢݇ £ = 3 ݅ + ݆ − ݇ £ . The acceleration vector is given by: = ? ?? ¡ 3 ¢݅ + ? ?? ¡ 1 ¢݆ + ? ?? ¡− 1 ¢݇ £ = 0 £ Problem 10 : The velocity vector is given by: = ? ?? ¡¡? − 1 ¢ 2 ¢݅ + ? ?? ¡ 2 ¢݆ + ? ?? ¡ 2 ? 3 − 3 ? 2 ¢݇ £ = 2 ¡? − 1 ¢݅ + + ¡ 6 ? 2 − 6 ?¢݇ £ . The speed is given by: ¤ ¤ = ¥ ¦ 2 ¡? − 1 ¢§ 2 + ¡ 6 ? 2 − 6 ?¢ 2 = 2 ¨? − 1 ¨© 1 + 9 ? 2 The particle stops when = 0 £ so when 2 ¡? − 1 ¢ = 6 ? 2 − 6 ? = 0 . Since these are all satisfies only by ? = 1 , this is the only time that the particle stops. Problem 14 : We have ª«? = ¬ ©¡−ª 2 sin ¡ª ? ¢¢ 2 + ¡ª ? cos ¡ª ? ¢¢ 2 ?? 1 = ¬ ª ? ?? 1 = ª − 1 This is the length of the arc of a unit circle from the point ¡ cos 1 , sin 1 ¢ to ¡ cos ª...
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This note was uploaded on 03/21/2010 for the course AMS 261 taught by Professor Fortmann during the Fall '08 term at SUNY Stony Brook.

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hw9-sol - Page 1 Assignment 9 100 points total Section 17.2...

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