{"id":6826,"date":"2024-04-15T02:34:44","date_gmt":"2024-04-15T02:34:44","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6826"},"modified":"2024-04-15T02:34:44","modified_gmt":"2024-04-15T02:34:44","slug":"a-shell-travelling-with-a-horizontal-velocity-of-100-m-sec-explodes-and-splits-into-two-parts-one-of-mass-10-kg-and-the-other-of-15-kg-the-15-kg-mass-drops-vertically-downward-with-initial-velocity","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-shell-travelling-with-a-horizontal-velocity-of-100-m-sec-explodes-and-splits-into-two-parts-one-of-mass-10-kg-and-the-other-of-15-kg-the-15-kg-mass-drops-vertically-downward-with-initial-velocity\/","title":{"rendered":"A shell travelling with a horizontal velocity of 100 m\/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. The 15 kg mass drops vertically downward with initial velocity of 100 m\/sec and the 10 kg mass begins to travel at an angle to the horizontal of tan-1x, where x is A. $$\\frac{3}{4}$$ B. $$\\frac{4}{5}$$ C. $$\\frac{5}{3}$$ D. $$\\frac{3}{5}$$"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6ab20d272594e\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    $$\frac{3}{4}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $$\frac{4}{5}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    $$\frac{5}{3}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    $$\frac{3}{5}$$                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is $\\boxed{\\frac{3}{5}}$.<\/p>\n<p>Let $m_1 = 10\\text{ kg}$ and $m_2 = 15\\text{ kg}$. The initial momentum of the shell is $p_i = m_1v_i = 10\\text{ kg}\\cdot 100\\text{ m\/s} = 1000\\text{ kg <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> m\/s}$. The final momentum of the system is $p_f = m_1v_1 <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> + m_2v_2$. Since the 15 kg mass drops vertically downward, $v_2 = 100\\text{ m\/s}$ and $m_2v_2 = 1500\\text{ kg m\/s}$. The 10 kg mass begins to travel at an angle to the horizontal, so $v_1$ has both horizontal and vertical components. The horizontal component of $v_1$ is $v_{1x} = 100\\text{ m\/s}$, and the vertical component of $v_1$ is $v_{1y}$. The total momentum of the system is conserved, so $p_i = p_f$. This gives us the equation $1000\\text{ kg m\/s} = 10\\text{ kg}v_{1x} + 15\\text{ kg}(100\\text{ m\/s})$. Solving for $v_{1x}$ gives us $v_{1x} = \\frac{3}{5}\\text{ m\/s}$. The angle to the horizontal is $\\tan^{-1}(v_{1y}\/v_{1x}) = \\boxed{\\frac{3}{5}}$.<\/p>\n<p>Each option is a possible value for $x$. Option A, $\\frac{3}{4}$, is not a possible value because it would give a negative value for $v_{1y}$. Option B, $\\frac{4}{5}$, is not a possible value because it would give a value for $v_{1x}$ that is greater than the initial horizontal velocity of the shell. Option C, $\\frac{5}{3}$, is not a possible value because it would give a value for $v_{1y}$ that is greater than the initial vertical velocity of the 15 kg mass. Option D, $\\frac{3}{5}$, is a possible value because it gives a value for $v_{1y}$ that is less than the initial vertical velocity of the 15 kg mass and a value for $v_{1x}$ that is less than the initial horizontal velocity of the shell.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[645],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A shell travelling with a horizontal velocity of 100 m\/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. The 15 kg mass drops vertically downward with initial velocity of 100 m\/sec and the 10 kg mass begins to travel at an angle to the horizontal of tan-1x, where x is A. $$\\frac{3}{4}$$ B. $$\\frac{4}{5}$$ C. $$\\frac{5}{3}$$ D. $$\\frac{3}{5}$$<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-shell-travelling-with-a-horizontal-velocity-of-100-m-sec-explodes-and-splits-into-two-parts-one-of-mass-10-kg-and-the-other-of-15-kg-the-15-kg-mass-drops-vertically-downward-with-initial-velocity\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A shell travelling with a horizontal velocity of 100 m\/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. The 15 kg mass drops vertically downward with initial velocity of 100 m\/sec and the 10 kg mass begins to travel at an angle to the horizontal of tan-1x, where x is A. $$\\frac{3}{4}$$ B. $$\\frac{4}{5}$$ C. $$\\frac{5}{3}$$ D. $$\\frac{3}{5}$$\" \/>\n<meta property=\"og:description\" content=\"Join Our Telegram Channel Subscribe on YouTube\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-shell-travelling-with-a-horizontal-velocity-of-100-m-sec-explodes-and-splits-into-two-parts-one-of-mass-10-kg-and-the-other-of-15-kg-the-15-kg-mass-drops-vertically-downward-with-initial-velocity\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T02:34:44+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A shell travelling with a horizontal velocity of 100 m\/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. 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