Pre-Calc Homework Solutions 441

# Pre-Calc Homework Solutions 441 - Cumulative Review 74(a...

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74. (a) r ( t ) 5 (155 cos 18 82 11.7) t i 1 (4 1 155 sin 18 8 t 2 16 t 2 ) j x ( t ) 5 (155 cos 18 82 11.7) t y ( t ) 5 4 1 155 sin 18 8 t 2 16 t 2 (b) y max 5 } (155 2 s ( i 3 n 2) 18 8 ) 2 }1 4 < 39.847 feet, reached at t max 5 } 155 3 si 2 n18 8 } < 1.497 sec (c) y ( t ) 5 0 when t < 3.075 sec (found using the quadratic formula), and then x < (155 cos 18 82 11.7)(3.075) < 417.307 ft. (d) Solve y ( t ) 5 25 using the quadratic formula: t 5 < 0.534 and 2.460 seconds. At those times, x 5 (155 cos 18 82 11.7) t equals < 72.406 and < 333.867 feet from home plate. (e) Yes, the batter has hit a home run. When the ball is 380 feet from home plate (at t < 2.800 seconds), it is approximately 12.673 feet off the ground and therefore clears the fence by at least two feet. 75. (a) r ( t ) 5 3 (155 cos 18 82 11.7) } 0. 1 09 } (1 2 e 2 0.09 t ) 4 i 1 3 4 1 1 } 155 0 s .0 in 9 18 8 } 2 (1 2 e 2 0.09 t ) 1 } 0. 3
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