A volleyball court measures 30- feet wide by 60-feet long. The net is located 30-feet from the serve line. Assume the server stands 31 feet from the net she serves the ball. The net is approximately 7. 5 feet from the ground. Write an equation that would show the path of a served ball that would clear the net and explain how you found your equation. Then document your equation.
Can you solve it in terms of an algebraic expression?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find an equation for the path of a served volleyball that clears the net, we can model the ball’s path as a projectile motion scenario. The equation of the path of the ball is a parabola since projectiles under the influence of gravity follow a parabolic trajectory. Here’s the step-by-step process and derivation:<\/p>\n\n\n\n Now, we solve the system of two equations:<\/p>\n\n\n\n We can multiply Equation 1 by 2 to align the ( b )-coefficients:<\/p>\n\n\n\n [ [ [ Now substitute ( a ) back into Equation 1:<\/p>\n\n\n\n [ Thus, the equation for the path of the ball is:<\/p>\n\n\n\n [ This equation represents the trajectory of the volleyball served from a height of 8 feet, ensuring it clears the net at 7.5 feet when it is 30 feet away from the server. The negative coefficient for ( x^2 ) indicates the ball follows a parabolic path, initially rising and then falling.<\/p>\n","protected":false},"excerpt":{"rendered":" A volleyball court measures 30- feet wide by 60-feet long. The net is located 30-feet from the serve line. Assume the server stands 31 feet from the net she serves the ball. The net is approximately 7. 5 feet from the ground. Write an equation that would show the path of a served ball that […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-150399","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150399","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=150399"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150399\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=150399"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=150399"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=150399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Assumptions and Known Values:<\/h3>\n\n\n\n
\n
y = ax^2 + bx + c
] where:<\/li>\n<\/ol>\n\n\n\n\n
Step-by-Step Derivation:<\/h3>\n\n\n\n
\n
y = ax^2 + bx + 8
]<\/li>\n\n\n\n
7.5 = a(30)^2 + b(30) + 8
]
Simplifying:
[
7.5 = 900a + 30b + 8
]
[
-0.5 = 900a + 30b \\quad \\text{(Equation 1)}
]<\/li>\n\n\n\n
0 = a(60)^2 + b(60) + 8
]
Simplifying:
[
0 = 3600a + 60b + 8
]
[
-8 = 3600a + 60b \\quad \\text{(Equation 2)}
]<\/li>\n<\/ol>\n\n\n\nSolving the System of Equations:<\/h3>\n\n\n\n
\n
1800a + 60b = -1
]
Subtracting Equation 1 from Equation 2:<\/p>\n\n\n\n
(3600a + 60b) – (1800a + 60b) = -8 – (-1)
]
Simplifying:<\/p>\n\n\n\n
1800a = -7
]
[
a = -\\frac{7}{1800}
]<\/p>\n\n\n\n
900\\left(-\\frac{7}{1800}\\right) + 30b = -0.5
]
[
-\\frac{7}{2} + 30b = -0.5
]
[
30b = -0.5 + \\frac{7}{2}
]
[
30b = -0.5 + 3.5 = 3
]
[
b = \\frac{3}{30} = \\frac{1}{10}
]<\/p>\n\n\n\nFinal Equation:<\/h3>\n\n\n\n
y = -\\frac{7}{1800}x^2 + \\frac{1}{10}x + 8
]<\/p>\n\n\n\n