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Consider a projectile launched at a heighth feet above the ground and at an angle with the horizontal. If the initial velocity is vo feet per second, the path of the projectile is modeled by the parametric equations x = t(v cos(0)) and y = h + (vo sin(0))t - 16t². The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit h = 2 feet above the ground. It leaves the bat at an angle of 0 degrees with the horizontal at a speed of 107 miles per hour (see figure). (a) Write a set of parametric equations for the path of the ball. (Write your equations in terms of t and 0. Enter your answers as a comma-separated list of equations.) |x=(157 cos (0))t, y = 3+ (157 sin(0))t — 16t² x O No 16 (b) Use a graphing utility to graph the path of the ball when 0 = 15°. Is the hit a home run? Yes 400 ft (c) Use a graphing utility to graph the path of the ball when 0 = 23°. Is the hit a home run? o Yes No X° (d) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run. (Round your answer to one decimal place.) 52.57 Need Help? Read It Watch It

Consider a projectile launched at a heighth feet above the ground and at an angle with the horizontal. If the initial velocity is vo feet per second, the path of the projectile is modeled by the parametric equations x = t(v cos(0)) and y = h + (vo sin(0))t - 16t². The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit h = 2 feet above the ground. It leaves the bat at an angle of 0 degrees with the horizontal at a speed of 107 miles per hour (see figure). (a) Write a set of parametric equations for the path of the ball. (Write your equations in terms of t and 0. Enter your answers as a comma-separated list of equations.) |x=(157 cos (0))t, y = 3+ (157 sin(0))t — 16t² x O No 16 (b) Use a graphing utility to graph the path of the ball when 0 = 15°. Is the hit a home run? Yes 400 ft (c) Use a graphing utility to graph the path of the ball when 0 = 23°. Is the hit a home run? o Yes No X° (d) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run. (Round your answer to one decimal place.) 52.57 Need Help? Read It Watch It

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.CT: Chapter Test
Problem 8CT
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Consider a projectile launched at a height h feet above the ground and at an angle with the horizontal. If the initial velocity is vo feet per second, the path of the projectile is modeled by the parametric equations x = t(v cos(0)) and y = h + (v₁ sin(0))t – 16t². The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit h = 2 feet above the ground. It leaves the bat at an angle of 0 degrees with the horizontal at a speed of 107 miles per hour (see figure). x=(157 cos Th ft (a) Write a set of parametric equations for the path of the ball. (Write your equations in terms of t and 0. Enter your answers as a comma-separated list of equations.) s(0) )t, y = 3+ (157 sin (0) )t — 16t² - x 400 ft $10 ft (b) Use a graphing utility to graph the path of the ball when 0 = 15°. Is the hit a home run? Yes No Read It (c) Use a graphing utility to graph the path of the ball when 0 = 23°. Is the hit a home run? Yes No (d) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run. (Round your answer to one decimal place.) 52.57 Need Help? Watch It
Transcribed Image Text:Consider a projectile launched at a height h feet above the ground and at an angle with the horizontal. If the initial velocity is vo feet per second, the path of the projectile is modeled by the parametric equations x = t(v cos(0)) and y = h + (v₁ sin(0))t – 16t². The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit h = 2 feet above the ground. It leaves the bat at an angle of 0 degrees with the horizontal at a speed of 107 miles per hour (see figure). x=(157 cos Th ft (a) Write a set of parametric equations for the path of the ball. (Write your equations in terms of t and 0. Enter your answers as a comma-separated list of equations.) s(0) )t, y = 3+ (157 sin (0) )t — 16t² - x 400 ft $10 ft (b) Use a graphing utility to graph the path of the ball when 0 = 15°. Is the hit a home run? Yes No Read It (c) Use a graphing utility to graph the path of the ball when 0 = 23°. Is the hit a home run? Yes No (d) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run. (Round your answer to one decimal place.) 52.57 Need Help? Watch It
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