{"id":16308,"date":"2025-06-11T08:44:33","date_gmt":"2025-06-11T08:44:33","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=16308"},"modified":"2025-06-11T08:44:51","modified_gmt":"2025-06-11T08:44:51","slug":"write-an-expression-in-terms-of-velocity-initial","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/write-an-expression-in-terms-of-velocity-initial\/","title":{"rendered":"write an expression in terms of velocity initial"},"content":{"rendered":"\n<p>write an expression in terms of velocity initial, theta and g for time it takes to travel max height<\/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<h3 class=\"wp-block-heading\"><strong>Expression for Time to Reach Maximum Height<\/strong><\/h3>\n\n\n\n<p>The time tt it takes for a projectile to reach <strong>maximum height<\/strong> is given by the following expression: t=visin\u2061(\u03b8)gt = \\frac{v_i \\sin(\\theta)}{g}<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>viv_i is the <strong>initial velocity<\/strong> of the projectile<\/li>\n\n\n\n<li>\u03b8\\theta is the <strong>angle of projection<\/strong> above the horizontal<\/li>\n\n\n\n<li>gg is the <strong>acceleration due to gravity<\/strong> (approximately 9.8\u2009m\/s29.8 \\, \\text{m\/s}^2 on Earth)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 words)<\/strong><\/h3>\n\n\n\n<p>In projectile motion, the time it takes to reach the <strong>maximum height<\/strong> is the moment when the <strong>vertical component<\/strong> of the velocity becomes <strong>zero<\/strong>. At launch, the object is projected with an initial velocity viv_i at an angle \u03b8\\theta above the horizontal. This velocity can be broken down into two components:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Horizontal component<\/strong>: vicos\u2061(\u03b8)v_i \\cos(\\theta) \u2013 constant throughout flight (ignoring air resistance)<\/li>\n\n\n\n<li><strong>Vertical component<\/strong>: visin\u2061(\u03b8)v_i \\sin(\\theta) \u2013 changes due to gravity<\/li>\n<\/ul>\n\n\n\n<p>As the projectile rises, gravity acts downward, reducing the vertical component of velocity. Eventually, the vertical velocity becomes zero\u2014this is the <strong>highest point<\/strong> (maximum height).<\/p>\n\n\n\n<p>To find the <strong>time to reach this point<\/strong>, we use the following kinematic equation for vertical motion: vf=vi+atv_f = v_i + a t<\/p>\n\n\n\n<p>At maximum height, the <strong>final vertical velocity<\/strong> vf=0v_f = 0. The <strong>acceleration<\/strong> aa is gravity, but acting downward, so a=\u2212ga = -g. The <strong>initial vertical velocity<\/strong> is visin\u2061(\u03b8)v_i \\sin(\\theta). Plugging in: 0=visin\u2061(\u03b8)\u2212gt0 = v_i \\sin(\\theta) &#8211; g t<\/p>\n\n\n\n<p>Solving for tt: t=visin\u2061(\u03b8)gt = \\frac{v_i \\sin(\\theta)}{g}<\/p>\n\n\n\n<p>This equation tells us that the time to reach max height depends <strong>directly<\/strong> on the initial vertical velocity and <strong>inversely<\/strong> on gravity. A greater angle \u03b8\\theta (closer to vertical) increases the vertical component of velocity, hence increasing time to max height. A larger gravitational force reduces that time. This formula is essential in physics and engineering for predicting projectile behavior.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>write an expression in terms of velocity initial, theta and g for time it takes to travel max height The correct answer and explanation is: Expression for Time to Reach Maximum Height The time tt it takes for a projectile to reach maximum height is given by the following expression: t=visin\u2061(\u03b8)gt = \\frac{v_i \\sin(\\theta)}{g} Where: [&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-16308","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16308","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=16308"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16308\/revisions"}],"predecessor-version":[{"id":16310,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16308\/revisions\/16310"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=16308"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=16308"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=16308"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}