{"id":15806,"date":"2025-06-10T19:18:30","date_gmt":"2025-06-10T19:18:30","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=15806"},"modified":"2025-06-10T19:18:36","modified_gmt":"2025-06-10T19:18:36","slug":"a-person-is-thrown-upward-from-a-height-of-2-meters-above-earths-surface-with-an-initial-velocity-of-50-m-s-and-the-only-force-acting-on-them-is-gravity-9-8-m-s2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-person-is-thrown-upward-from-a-height-of-2-meters-above-earths-surface-with-an-initial-velocity-of-50-m-s-and-the-only-force-acting-on-them-is-gravity-9-8-m-s2\/","title":{"rendered":"A person is thrown upward from a height of 2 meters above Earth\u2019s surface with an initial velocity of 50 m\/s, and the only force acting on them is gravity (9.8 m\/s2 )"},"content":{"rendered":"\n<p>A person is thrown upward from a height of 2 meters above Earth\u2019s surface with an initial velocity of 50 m\/s, and the only force acting on them is gravity (9.8 m\/s2 ).<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>Okay, the question implies a need to analyze the motion of the person under gravity. The most common calculation requested in such a scenario is the time it takes for the person to reach a specific point, such as their maximum height or, more dramatically, the ground. Let&#8217;s calculate the time it takes for the person to hit the ground (y=0).<\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><\/p>\n\n\n\n<p>The positive time it takes for the person to hit the ground is approximately <strong>10.24 seconds<\/strong>.<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>This problem involves one-dimensional motion under constant acceleration due to gravity. We can use kinematic equations to describe the person&#8217;s position over time.<\/p>\n\n\n\n<p>Let&#8217;s define the upward direction as positive and the downward direction as negative.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial height (y\u2080): +2 meters (above the ground)<\/li>\n\n\n\n<li>Initial velocity (v\u2080): +50 m\/s (upward)<\/li>\n\n\n\n<li>Acceleration due to gravity (a): -9.8 m\/s\u00b2 (downward)<\/li>\n\n\n\n<li>Target height (y): 0 meters (the ground)<\/li>\n<\/ul>\n\n\n\n<p>The relevant kinematic equation relating position, initial position, initial velocity, acceleration, and time (t) is:<br>y = y\u2080 + v\u2080t + (1\/2)at\u00b2<\/p>\n\n\n\n<p>We want to find the time t when the person reaches the ground, so we set y = 0:<br>0 = 2 + 50t + (1\/2)(-9.8)t\u00b2<\/p>\n\n\n\n<p>This simplifies to a quadratic equation in terms of t:<br>0 = 2 + 50t &#8211; 4.9t\u00b2<\/p>\n\n\n\n<p>Rearranging into the standard quadratic form (at\u00b2 + bt + c = 0):<br>-4.9t\u00b2 + 50t + 2 = 0<br>or<br>4.9t\u00b2 &#8211; 50t &#8211; 2 = 0<\/p>\n\n\n\n<p>We can solve for t using the quadratic formula: t = [-b \u00b1 sqrt(b\u00b2 &#8211; 4ac)] \/ (2a)<br>Here, a = 4.9, b = -50, and c = -2.<\/p>\n\n\n\n<p>t = [ -(-50) \u00b1 sqrt((-50)\u00b2 &#8211; 4 * 4.9 * -2) ] \/ (2 * 4.9)<br>t = [ 50 \u00b1 sqrt(2500 + 39.2) ] \/ 9.8<br>t = [ 50 \u00b1 sqrt(2539.2) ] \/ 9.8<br>t = [ 50 \u00b1 50.39 ] \/ 9.8<\/p>\n\n\n\n<p>This gives two possible solutions for t:<br>t\u2081 = (50 + 50.39) \/ 9.8 = 100.39 \/ 9.8 \u2248 10.24 seconds<br>t\u2082 = (50 &#8211; 50.39) \/ 9.8 = -0.39 \/ 9.8 \u2248 -0.04 seconds<\/p>\n\n\n\n<p>Since time cannot be negative in this context (the motion starts at t=0), the physically meaningful answer is the positive one. Therefore, it takes approximately <strong>10.24 seconds<\/strong> for the person to hit the ground after being thrown upward from a height of 2 meters.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A person is thrown upward from a height of 2 meters above Earth\u2019s surface with an initial velocity of 50 m\/s, and the only force acting on them is gravity (9.8 m\/s2 ). The correct answer and explanation is: Okay, the question implies a need to analyze the motion of the person under gravity. The [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-15806","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15806","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=15806"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15806\/revisions"}],"predecessor-version":[{"id":15807,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15806\/revisions\/15807"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=15806"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=15806"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=15806"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}