{"id":182882,"date":"2025-01-15T06:19:48","date_gmt":"2025-01-15T06:19:48","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=182882"},"modified":"2025-01-15T06:19:50","modified_gmt":"2025-01-15T06:19:50","slug":"in-1939-or-1940-emanuel-zucchini-took-his-human-cannonball-act-to-an-extreme","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/15\/in-1939-or-1940-emanuel-zucchini-took-his-human-cannonball-act-to-an-extreme\/","title":{"rendered":"In 1939 or 1940, Emanuel Zucchini took his human-cannonball act to an extreme"},"content":{"rendered":"\n<p>In 1939 or 1940, Emanuel Zucchini took his human-cannonball act to an extreme: After being shot from a cannon, he soared over three Ferris wheels and into a net (Fig. 4.42)<br>(a) Treating him as a particle, calculate his clearance over the first wheel.<br>(b) If he reached maximum height over the middle wheel, by how much did he clear it?<br>(c) How far from the cannon should the net&#8217;s center have been positioned (neglect airdrag)?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/01\/image-214.png\" alt=\"\" class=\"wp-image-182883\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>In 1939 or 1940, Emanuel Zacchini performed a human-cannonball act where he was launched from a cannon, soaring over three Ferris wheels before landing in a net. To analyze this scenario, we can treat Zacchini as a particle and apply principles of projectile motion.<\/p>\n\n\n\n<p><strong>Given:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Launch speed ((v_0)): 29 m\/s<\/li>\n\n\n\n<li>Launch angle ((\\theta)): 52\u00b0<\/li>\n\n\n\n<li>Acceleration due to gravity ((g)): 9.81 m\/s\u00b2<\/li>\n<\/ul>\n\n\n\n<p><strong>(a) Clearance over the first wheel:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Horizontal and Vertical Components of Velocity:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Horizontal velocity ((v_{0x})): (v_0 \\times \\cos(\\theta))<\/li>\n\n\n\n<li>Vertical velocity ((v_{0y})): (v_0 \\times \\sin(\\theta)) Calculating these components:<\/li>\n\n\n\n<li>(v_{0x} = 29 \\, \\text{m\/s} \\times \\cos(52^\\circ) \\approx 29 \\, \\text{m\/s} \\times 0.6157 \\approx 17.85 \\, \\text{m\/s})<\/li>\n\n\n\n<li>(v_{0y} = 29 \\, \\text{m\/s} \\times \\sin(52^\\circ) \\approx 29 \\, \\text{m\/s} \\times 0.7880 \\approx 22.85 \\, \\text{m\/s})<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Time to Reach the First Wheel:<\/strong><br>Assuming the first Ferris wheel is 20 meters away horizontally:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Time ((t)) to reach the first wheel: (t = \\frac{\\text{horizontal distance}}{v_{0x}} = \\frac{20 \\, \\text{m}}{17.85 \\, \\text{m\/s}} \\approx 1.12 \\, \\text{s})<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Vertical Position at (t = 1.12 \\, \\text{s}):<\/strong><br>The vertical position ((y)) is given by:<br>[<br>y = v_{0y} \\times t &#8211; \\frac{1}{2} \\times g \\times t^2<br>]<br>Substituting the known values:<br>[<br>y = 22.85 \\, \\text{m\/s} \\times 1.12 \\, \\text{s} &#8211; \\frac{1}{2} \\times 9.81 \\, \\text{m\/s}^2 \\times (1.12 \\, \\text{s})^2<br>]<br>[<br>y \\approx 25.6 \\, \\text{m} &#8211; 6.1 \\, \\text{m} \\approx 19.5 \\, \\text{m}<br>]<br>Therefore, Zacchini&#8217;s clearance over the first wheel is approximately 19.5 meters.<\/li>\n<\/ol>\n\n\n\n<p><strong>(b) Clearance over the middle wheel:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Time to Reach Maximum Height:<\/strong><br>At maximum height, the vertical velocity component becomes zero. The time to reach maximum height ((t_{\\text{max}})) is:<br>[<br>t_{\\text{max}} = \\frac{v_{0y}}{g} = \\frac{22.85 \\, \\text{m\/s}}{9.81 \\, \\text{m\/s}^2} \\approx 2.33 \\, \\text{s}<br>]<br>Since the middle Ferris wheel is at half the horizontal range, the time to reach it is half of (t_{\\text{max}}):<br>[<br>t_{\\text{middle}} = \\frac{t_{\\text{max}}}{2} \\approx 1.165 \\, \\text{s}<br>]<br>At this time, the horizontal distance covered is:<br>[<br>x = v_{0x} \\times t_{\\text{middle}} \\approx 17.85 \\, \\text{m\/s} \\times 1.165 \\, \\text{s} \\approx 20.8 \\, \\text{m}<br>]<br>Therefore, the middle Ferris wheel is approximately 20.8 meters away horizontally.<\/li>\n\n\n\n<li><strong>Vertical Position at (t = 1.165 \\, \\text{s}):<\/strong><br>Using the vertical motion equation:<br>[<br>y = v_{0y} \\times t_{\\text{middle}} &#8211; \\frac{1}{2} \\times g \\times (t_{\\text{middle}})^2<br>]<br>Substituting the known values:<br>[<br>y = 22.85 \\, \\text{m\/s} \\times 1.165 \\, \\text{s} &#8211; \\frac{1}{2} \\times 9.81 \\, \\text{m\/s}^2 \\times (1.165 \\, \\text{s})^2<br>]<br>[<br>y \\approx 26.6 \\, \\text{m} &#8211; 6.6 \\, \\text{m} \\approx 20.0 \\, \\text{m}<br>]<br>Therefore, Zacchini&#8217;s clearance over the middle wheel is approximately 20.0 meters.<\/li>\n<\/ol>\n\n\n\n<p><strong>(c) Distance to Position the Net:<\/strong><\/p>\n\n\n\n<p>The net should be positioned at the point where Zacchini lands, which is at the horizontal range of the projectile. The total time of flight ((t_{\\text{total}})) is twice the time to reach maximum height:<br>[<br>t_{\\text{total}} = 2 \\times t_{\\text{max}} \\approx 2 \\times 2.33 \\, \\text{s} \\approx 4.66 \\, \\text{s}<br>]<br>The horizontal range ((R)) is:<br>[<br>R = v_{0x} \\times t_{\\text{total}} \\approx 17.85 \\, \\text{m\/s} \\times 4.66 \\, \\text{s} \\approx 83.3 \\, \\text{m}<br>]<br>Therefore, the net&#8217;s center should be positioned approximately 83.3 meters from the cannon.<\/p>\n\n\n\n<p><strong>Conclusion:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(a)<\/strong> Zacchini&#8217;s clearance over the first Ferris wheel is approximately 19.5 meters.<\/li>\n\n\n\n<li><strong>(b)<\/strong> His clearance over the middle Ferris wheel is approximately 20.0 meters.<\/li>\n\n\n\n<li><strong>(c)<\/strong> The net&#8217;s center should be positioned approximately 83.3 meters from the cannon.<\/li>\n<\/ul>\n\n\n\n<p>These calculations assume ideal projectile motion without air resistance.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In 1939 or 1940, Emanuel Zucchini took his human-cannonball act to an extreme: After being shot from a cannon, he soared over three Ferris wheels and into a net (Fig. 4.42)(a) Treating him as a particle, calculate his clearance over the first wheel.(b) If he reached maximum height over the middle wheel, by how much [&hellip;]<\/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 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