A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 2.80 s for the ball to reach its maximum height. <\/p>\n\n\n\n
(a) Find its initial velocity. m\/s (upward) <\/p>\n\n\n\n
(b) Find the height it reaches.<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n We will solve this using kinematic equations. Given that the baseball takes 2.80 s<\/strong> to reach its maximum height, we analyze the motion under gravity.<\/p>\n\n\n\n Using the equation:<\/p>\n\n\n\n [ [ [ So, the initial velocity is 27.47 m\/s (upward)<\/strong>.<\/p>\n\n\n\n Using another kinematic equation:<\/p>\n\n\n\n [ Since ( v = 0 ) at max height,<\/p>\n\n\n\n [ [ [ [ So, the maximum height reached is 38.47 m<\/strong>.<\/p>\n\n\n\n The problem involves one-dimensional motion under gravity. When the baseball is hit, it moves upward until it reaches a maximum height, where its velocity becomes zero before coming back down. The time taken to reach the highest point is given as 2.80 seconds<\/strong>. Using this information, we can calculate its initial velocity<\/strong> by applying the first kinematic equation: To find the maximum height<\/strong>, we use another kinematic equation that relates velocity, acceleration, and displacement. Since the final velocity at the peak is zero, we use: Thus, the baseball reaches a height of 38.47 m<\/strong> before coming back down.<\/p>\n","protected":false},"excerpt":{"rendered":" A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 2.80 s for the ball to reach its maximum height. (a) Find its initial velocity. m\/s (upward) (b) Find the height it reaches. The correct answer and explanation is : We will solve […]<\/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-201986","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/201986","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=201986"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/201986\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=201986"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=201986"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=201986"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Understanding the Motion<\/h3>\n\n\n\n
\n
v = u + at
] where:<\/li>\n\n\n\n(a) Finding Initial Velocity<\/h3>\n\n\n\n
0 = u – (9.81)(2.80)
]<\/p>\n\n\n\n
u = (9.81)(2.80)
]<\/p>\n\n\n\n
u = 27.47 \\, \\text{m\/s}
]<\/p>\n\n\n\n
\n\n\n\n(b) Finding Maximum Height<\/h3>\n\n\n\n
v^2 = u^2 + 2as
]<\/p>\n\n\n\n
0 = u^2 + 2(-9.81) s
]<\/p>\n\n\n\n
s = \\frac{u^2}{2g} = \\frac{(27.47)^2}{2(9.81)}
]<\/p>\n\n\n\n
s = \\frac{754.56}{19.62}
]<\/p>\n\n\n\n
s = 38.47 \\, \\text{m}
]<\/p>\n\n\n\n
\n\n\n\nExplanation (300 words)<\/h3>\n\n\n\n
[
v = u + at
]
Since the velocity at the peak is zero, we rearrange to solve for ( u ), considering gravity as ( -9.81 \\, \\text{m\/s}^2 )<\/strong>. Plugging in the values, we find that the initial velocity is 27.47 m\/s<\/strong>.<\/p>\n\n\n\n
[
v^2 = u^2 + 2as
]
Solving for ( s ), we substitute the values and get 38.47 meters<\/strong>.<\/p>\n\n\n\n