A ball is thrown across a playing field from a height of h = 6 ft above the ground at an angle of 45° to the horizontal at the speed of 20 ft/s. It can be deduced from physical principles that the path of the ball is modeled by the function y = − 32 (20)2 x2 + x + 6 where x is the distance in feet that the ball has traveled horizontally. (a) Find the maximum height attained by the ball. (Round your answer to three decimal places.)ft(b) Find the horizontal distance the ball has traveled when it hits the ground. (Round your answer to one decimal place.)ft
A ball is thrown across a playing field from a height of h = 6 ft above the ground at an angle of 45° to the horizontal at the speed of 20 ft/s. It can be deduced from physical principles that the path of the ball is modeled by the function y = − 32 (20)2 x2 + x + 6 where x is the distance in feet that the ball has traveled horizontally. (a) Find the maximum height attained by the ball. (Round your answer to three decimal places.)ft(b) Find the horizontal distance the ball has traveled when it hits the ground. (Round your answer to one decimal place.)ft
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
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A ball is thrown across a playing field from a height of h = 6 ft above the ground at an angle of 45° to the horizontal at the speed of 20 ft/s. It can be deduced from physical principles that the path of the ball is modeled by the function
y = −
x2 + x + 6
32 |
(20)2 |
where x is the distance in feet that the ball has traveled horizontally.
(a) Find the maximum height attained by the ball. (Round your answer to three decimal places.)
ft
(b) Find the horizontal distance the ball has traveled when it hits the ground. (Round your answer to one decimal place.)
ft
ft
(b) Find the horizontal distance the ball has traveled when it hits the ground. (Round your answer to one decimal place.)
ft
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Step 1: Given information
VIEWStep 2: Vertical co-ordinate of highest point (h,k)
VIEWStep 3: Horizontal co-ordinate of highest point. (h,k)
VIEWStep 4: Equation of motion, ( parabolic path)
VIEWStep 5: Value of maximum horizontal distance covered. (When ball hits the ground)
VIEWStep 6: Graphical presentation of the situation.
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