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Pre-Calc Homework Solutions 417

Pre-Calc Homework Solutions 417 - Section 10.4 23 Angle is...

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23. Angle is a < 62° (measurements may vary slightly). For flight time t 5 } 2 v 0 g sin a } 5 1 sec, y max 5 } ( v 0 s 2 in g a ) 2 } 5 } 1 8 } gt 2 5 } 1 8 } (32)(1) 2 5 4 ft (independent of the measured angle). v 0 5 } 2 s g in t a } , so speed of engine 5 v 0 cos a 5 } 2 t g an t a } < } 2 ta 3 n 2( ( 1 6 ) 2°) } < 8.507 ft/sec (changes with the angle). 24. The height of A is given by y A 5 ( v sin a ) t 2 } 1 2 } gt 2 and the height of B is given by y B 5 R tan a 2 } 1 2 } gt 2 . The second terms in y A and y B 1 2 } 1 2 } gt 2 2 are equal for any value of t . But A moves R units horizontally to B ’s line of fall in } v co R s a } time units, and the first terms in y A and y B are also equal at that time: ( v sin a ) 1 } v co R s a } 2 5 R tan a . Therefore, A and B will always be at the same height when A reaches B ’s line of fall. 25. (a) x 5 ( v 0 cos u ) t y 5 ( v 0 sin u ) t 2 } 1 2 } gt 2 x 5 R cos b R cos b 5 ( v 0 cos u ) t t 5 } v R 0 c c o o s s b u } . Then y 5 2 R sin b 2 R sin b 5 } ( v 0 si v n 0 u c ) o R s u cos b } 2 } g 2 } } R v 0 2 2 c c o o s s 2 2 b u } R 5 } g c 2 o v s 0 2 2 b } cos u sin ( u 1 b ).
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