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Pre-Calc Homework Solutions 439

# Pre-Calc Homework Solutions 439 - Chapter 10 Review dr =(e...

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54. v ( t ) 5 } d d r t } = ( e t cos t 2 e t sin t ) i 1 ( e t sin t 1 e t cos t ) j a ( t ) 5 } d d x t } 5 ( e t cos t 2 e t sin t 2 e t sin t 2 e t cos t ) i 1 ( e t sin t 1 e t cos t 1 e t cos t 2 e t sin t ) j 5 ( 2 2 e t sin t ) i 1 (2 e t cos t ) j r ( t ) ? a ( t ) 5 ( e t cos t )( 2 2 e t sin t ) 1 ( e t sin t )(2 e t cos t ) 5 0 for all t . The angle between r and a is always 90 8 . 55. 1 E 1 0 (3 1 6 t ) dt 2 i 1 1 E 1 0 6 p cos p t dt 2 j 5 3 3 t 1 3 t 2 4 i 1 3 6 sin p t 4 j 5 6 i 56. 1 E e 2 e } 2 l t n t } dt 2 i 1 1 E e 2 e } t l 1 n t } dt 2 j 5 3 ln 2 t 4 i 1 3 ln (ln t ) 4 j 5 3 i 1 (ln 2) j 57. r ( t ) 5 E } d d r t } dt 5 (cos t ) i 1 (sin t ) j 1 C r (0) 5 i 1 C 5 j , so C 5 2 i 1 j , and r ( t ) 5 (cos t 2 1) i 1 (sin t 1 1) j 58. r ( t ) 5 E } d d r t } dt 5 (tan 2 1 t ) i 1 ˇ t 2 w 1 w 1 w j 1 C r (0) 5 j 1 C 5 i 1 j , so C 5 i and r ( t ) 5 (tan 2 1 t 1 1) i 1 ˇ t 2 w 1 w 1 w j 59. } d d r t } 5 E } d dt 2 2 r } dt 5 2 t j 1 C 1 , r ( t ) 5 E } d d r t } dt 5 t 2 j 1 C 1 t 1 C 2 } d d r t } ) t 5 0 5 C 1 5 0 , so r ( t ) 5 t 2 j 1 C 2 . And r (0) 5 C 2 5 i , so r ( t ) 5 i 1 t 2 j 60.
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