Pre-Calc Homework Solutions 410

Pre-Calc Homework Solutions 410 - 410 5(a Section 10.3 8(a...

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Unformatted text preview: 410 5. (a) Section 10.3 8. (a) [ 6, 6] by [ 4, 4] [ 6, 6] by [ 3, 5] (b) v(t) d (2 cos t)i dt d (3 sin t)j dt (b) v(t) ( 2 sin t)i a(t) d ( 2 sin t)i dt (3 cos t)j d (3 cos t)j dt ( 2 cos t)i (c) v (3 sin t)j ( 2)2 1, 0 02 2, a(t) (c) v(1) d d 2 (2 ln (t 1))i (t )j dt dt 2 i (2t)j t 1 d 2 d 2 i (2t)j i dt t 1 dt (t 1)2 2j 2 2, 0 ; speed 1 2 1, 2 ; speed 1 5 12 1 5 22 , 2 5 5, direction (d) Velocity 6. (a) 2, 0 1, 0 direction (d) Velocity 9. v(t) (cos t)i 1, 2 1 5 2 5 (2t , 2 5 sin t)j, r(0) j and v(0) i. So the slope is zero (the velocity vector is horizontal). [ 4.5, 4.5] by [ 3, 3] (a) The horizontal line through (0, (b) The vertical line through (0, 10. v(t) r v 22 2, 4 4 1): y 1): x 0. 1. (b) v(t) d (cos 2t)i dt d (2 sin t)j dt ( 2 sin 2t)i a(t) d ( 2 sin 2t)i dt (2 cos t)j d (2 cos t)j dt ( 2 sin t)i ( 2 ( 3 2 3 x 2 3 2 2 x 3 (3 cos t)j, 3 2 3 2 3)i 2)i 1 j and j. So the slope is 3/ 2 2 3 . 2 ( 4 cos t)i (c) v(0) 0, 2 ; speed 1 0, 2 2 (2 sin t)j 02 0, 1 (a) y y 1 6 2 2 direction (d) Velocity 7. (a) 3 [x 2 7 ( 2 3)] or 2 0, 1 (b) y y [ 6, 6] by [ 4, 4] 2 1 2 [x 3 ( 2 3)] or 5 2 18 6 2 (b) v(t) a(t) d d (sec t)i (tan t)i (sec t tan t)i dt dt d d (sec t tan t)i (sec2 t)j dt dt 11. (sec2 t)j 1 (6 6t 3i /4 6t) dt i 1 3 2t 3/2 j 1 2 t dt j 3t 2 i 1 2 (sec t tan2 t sec3 t)i (2 sec2 t tan t)j 2 5 , 3 (4 2 2)j /4 (c) v 2 4 , ; speed 3 3 3 2 4 , direction 2 5 3 3 6 2 5 3 1 5 2 2 4 2 3 3 1 2 12. sin t dt i /4 (1 /4 cos t) dt j /4 , /4 5 2 5 5 cos t 2 j i /4 t sin t j /4 (d) Velocity , 2 ...
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