![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-904-1024x747.png\")
<\/figure>\n\n\n\nThe pellet will hit the ground 8.02 seconds<\/strong> after being fired.<\/p>\n\n\n\n This is a kinematics problem where we analyze the motion of a pellet fired straight up from a cliff. The pellet follows a parabolic trajectory under the influence of gravity.<\/p>\n\n\n\n The general equation of motion in free fall is:<\/p>\n\n\n\n [ Since we need to find when the pellet hits the ground, we set ( y = 0 ):<\/p>\n\n\n\n [ Rewriting:<\/p>\n\n\n\n [ Using the quadratic formula:<\/p>\n\n\n\n [ Solving this gives two values for ( t ):<\/p>\n\n\n\n [ Thus, the pellet hits the ground after 8.02 seconds<\/strong>.<\/p>\n\n\n\n The plot above visually represents the pellet\u2019s motion, showing that it first rises, reaches a peak, and then falls to the ground.<\/p>\n","protected":false},"excerpt":{"rendered":" From the edge of a cliff, a gun fires a pellet straight upward. The pellet\u2019s speed after leaving the gun is 30 m\/s; the cliff is 75 meters tall. Assume that the ground is at height = 0 and that the positive direction is upward. At what time does the pellet hit the ground? The […]<\/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-199556","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199556","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=199556"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199556\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
Step 1: Identify Given Information<\/h4>\n\n\n\n
\n
Step 2: Use the Kinematic Equation<\/h4>\n\n\n\n
y = h + v_0 t – \\frac{1}{2} g t^2
]<\/p>\n\n\n\n
0 = 75 + 30t – \\frac{1}{2} (9.81) t^2
]<\/p>\n\n\n\n
4.905t^2 – 30t – 75 = 0
]<\/p>\n\n\n\nStep 3: Solve the Quadratic Equation<\/h4>\n\n\n\n
t = \\frac{-(-30) \\pm \\sqrt{(-30)^2 – 4(4.905)(-75)}}{2(4.905)}
]<\/p>\n\n\n\n
t_1 = -3.06 \\quad \\text{(negative, not valid)}
]
[
t_2 = 8.02 \\quad \\text{(valid, as time cannot be negative)}
]<\/p>\n\n\n\n