Turito Academy

Test Prep

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Time of flight. <img src="data:image/png;base64,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" class="Wirisformula" alt="T equals fraction numerator 2 u sin invisible function application theta over denominator g end fraction" width="91" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»T«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mi»u«/mi»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»θ«/mi»«/mrow»«/mrow»«/mrow»«mrow»«mi»g«/mi»«/mrow»«/mfrac»«/math»'/> Horizontal range, <img src="data:image/png;base64,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" class="Wirisformula" alt="R equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction" width="99" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»R«/mi»«mo»=«/mo»«mfrac»«mrow»«msup»«mrow»«mi»u«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»2«/mn»«mi»θ«/mi»«/mrow»«/mrow»«/mrow»«mrow»«mi»g«/mi»«/mrow»«/mfrac»«/math»'/> Change in angular momentum, <img src="data:image/png;base64,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" class="Wirisformula" alt="open vertical bar d stack L with rightwards arrow on top close vertical bar equals open vertical bar stack L with rightwards arrow on top subscript f end subscript minus stack L with rightwards arrow on top subscript i end subscript close vertical bar" width="114" height="26" style="vertical-align:-6px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced open=¨|¨ close=¨|¨ separators=¨|¨»«mrow»«mi»d«/mi»«mover accent=¨true¨»«mrow»«mi»L«/mi»«/mrow»«mo»→«/mo»«/mover»«/mrow»«/mfenced»«mo»=«/mo»«mfenced open=¨|¨ close=¨|¨ separators=¨|¨»«mrow»«msub»«mrow»«mover accent=¨true¨»«mrow»«mi»L«/mi»«/mrow»«mo»→«/mo»«/mover»«/mrow»«mrow»«mi»f«/mi»«/mrow»«/msub»«mo»-«/mo»«msub»«mrow»«mover accent=¨true¨»«mrow»«mi»L«/mi»«/mrow»«mo»→«/mo»«/mover»«/mrow»«mrow»«mi»i«/mi»«/mrow»«/msub»«/mrow»«/mfenced»«/math»'/> about point of projection <img src="data:image/png;base64,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" class="Wirisformula" alt="equals left parenthesis m u sin invisible function application theta right parenthesis cross times fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction" width="175" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»=«/mo»«mo»(«/mo»«mi»m«/mi»«mi»u«/mi»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»θ«/mi»«/mrow»«/mrow»«mo»)«/mo»«mo»×«/mo»«mfrac»«mrow»«msup»«mrow»«mi»u«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»2«/mn»«mi»θ«/mi»«/mrow»«/mrow»«/mrow»«mrow»«mi»g«/mi»«/mrow»«/mfrac»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="equals fraction numerator m u to the power of 3 end exponent sin invisible function application theta sin invisible function application 2 theta over denominator g end fraction" width="137" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»=«/mo»«mfrac»«mrow»«mi»m«/mi»«msup»«mrow»«mi»u«/mi»«/mrow»«mrow»«mn»3«/mn»«/mrow»«/msup»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»θ«/mi»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»2«/mn»«mi»θ«/mi»«/mrow»«/mrow»«/mrow»«/mrow»«/mrow»«mrow»«mi»g«/mi»«/mrow»«/mfrac»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="T o r q u e blank open vertical bar stack tau with rightwards arrow on top close vertical bar equals fraction numerator c h a n g e blank i n blank a n g u l a r blank m o m e n t u m over denominator t i m e blank o f blank f l i g h t end fraction" width="344" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»T«/mi»«mi»o«/mi»«mi»r«/mi»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mi» «/mi»«mfenced open=¨|¨ close=¨|¨ separators=¨|¨»«mrow»«mover accent=¨true¨»«mrow»«mi»τ«/mi»«/mrow»«mo»→«/mo»«/mover»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»c«/mi»«mi»h«/mi»«mi»a«/mi»«mi»n«/mi»«mi»g«/mi»«mi»e«/mi»«mi» «/mi»«mi»i«/mi»«mi»n«/mi»«mi» «/mi»«mi»a«/mi»«mi»n«/mi»«mi»g«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»r«/mi»«mi» «/mi»«mi»m«/mi»«mi»o«/mi»«mi»m«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»u«/mi»«mi»m«/mi»«/mrow»«mrow»«mi»t«/mi»«mi»i«/mi»«mi»m«/mi»«mi»e«/mi»«mi» «/mi»«mi»o«/mi»«mi»f«/mi»«mi» «/mi»«mi»f«/mi»«mi»l«/mi»«mi»i«/mi»«mi»g«/mi»«mi»h«/mi»«mi»t«/mi»«/mrow»«/mfrac»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADYAAAArCAYAAAAzDXuYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAeOiuv/QAAAYpJREFUeNpjYBg6YD4Q8wyExf9pbP5sIL4FxOb0dge1DMyCmoUL/wFitaHoMXwxdheITYdqjFGax4acxwbMHaMewwK+ATETGXKD2mMqQHyJDLlB77EAIF5Ohtyg8hioVJsExB+A+AcQrwHiKUBcjkN9PR65QeMxUD7ZD8SJUDYf1OH/oTGDDazCIzdoPFaLI/RBzSRpHHrwyQ0ajz3GUsEyQUs9XDH8ZbAX9wZAfBCLuDk0eTKQKDdoPBYExIuxiEdCm0oMJMoNGo8FQAsCdADybBoOPZOgBc2g9hgXEF+DJkkQMAbiLUD8FIi9cOhZB8QeQ6FJJQ51LKj+Og7EjkD8Dog5cKh/h6dPxjbaCB712BD22H8i8GiMDUeP/acjHk2Ko0lx1GOjHhseHgN1Jn8RKKh+MQzR4TdkAJpsuDAckyKoQ7p0OHqsEYhLhqPHQOOMfsPRY6D5L8nh5jEWBvKG2wa9xywZyBtuG/QeI3e4bdB7DDTcljwcPQYawfIajh7DNxQ32giGuQMAymLNcXoycr4AAADmdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPj08L21vPjxtZmVuY2VkIGNsb3NlPSJ8IiBvcGVuPSJ8IiBzZXBhcmF0b3JzPSJ8Ij48bWZyYWM+PG1yb3c+PG1pPmQ8L21pPjxtb3ZlciBhY2NlbnQ9InRydWUiPjxtaT5MPC9taT48bW8+JiN4MjE5Mjs8L21vPjwvbW92ZXI+PC9tcm93PjxtaT5UPC9taT48L21mcmFjPjwvbWZlbmNlZD48L21hdGg+M5ggrgAAAABJRU5ErkJggg==" class="Wirisformula" alt="equals open vertical bar fraction numerator d stack L with rightwards arrow on top over denominator T end fraction close vertical bar" width="54" height="43" style="vertical-align:-13px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»=«/mo»«mfenced open=¨|¨ close=¨|¨ separators=¨|¨»«mrow»«mfrac»«mrow»«mi»d«/mi»«mover accent=¨true¨»«mrow»«mi»L«/mi»«/mrow»«mo»→«/mo»«/mover»«/mrow»«mrow»«mi»T«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«/math»'/>

Average torque on a projectile of mass <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAKCAYAAAC9vt6cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAI5JREFUeNpjYECAeiAuB2JxIJ4ExC+B+DkQe0HlBYG4D4jfAfEnIK5kQAOroIacAeJIIGYBYnkgvg/EkkB8EIjDoeKyQPwDahkc3ALivVCbkMFTIJ6NQ1wSxmEC4m9AzIWmiJA4HJgD8X4GTEC0OMjP87EoJFocFOppWBQSLb4OKbrIEgfFLQcWhaSKkw4A8RgiEla1vLMAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPm08L21pPjwvbWF0aD5oJvHsAAAAAElFTkSuQmCC" class="Wirisformula" alt="m" width="16" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»m«/mi»«/math»'/>, initial speed <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAKCAYAAABi8KSDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAG1JREFUeNpjYECAeiAuZ8AEWMVXAXEAFsVYxW8BsTQWxRjiTED8DYtCrOLmQLwfi2Ks4pFAPB+L4nhs4hOAOA9NzBSInwNxMrbgWQh1oyiUPwWI1wGxF7piQSDeAcS/gPggEPtAxd8BMQcDOQAALoQVIlpjITsAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnU8L21pPjwvbWF0aD6GIoRbAAAAAElFTkSuQmCC" class="Wirisformula" alt="u" width="11" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»u«/mi»«/math»'/> and angles of projection <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=" class="Wirisformula" alt="theta" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»θ«/mi»«/math»'/>, between initial and final position <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIVJREFUeNpjYMAEP4D4PxR/AeJVQOyIRR2DChBfQOKzAbELEN8HYi10xQFAvBSLIclAXIIuWI9NEAg6gDgHXRDkPj80MVEgvgXEwuiKQYKSSHxjID6KzYNMQPwHGgrvoIqa0TTDgTkQ72cgEkQC8XxiFU8C4jRiFa8DYi9iFYM8xcFALQAAM/sYFg8AKnAAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPlA8L21pPjwvbWF0aD4oc3y9AAAAAElFTkSuQmCC" class="Wirisformula" alt="P" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»P«/mi»«/math»'/> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAOCAYAAAD0f5bSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAALtJREFUeNpjYMAO3IB4BxB/A+IfQHwYiB0Z8IAOIN4AxKZAzATFfkD8EoitsWnIA+KZOAwD2XQcXVAWiK9ATcYFPgAxG7JAKxDnMOAHu4HYAFkAZIs8AU0PgZgLxmGChhQ+wAJ1HorAJwKagoB4IbrgNwKBcBTdPwxQUxJxaKgE4i5sEhpA/BiI46HOBQE9IF4MDVmcwByI90OTDgj/B+IsBhJBOBA/B+IzQJwMxKLEauQB4nIgvgZNyAwAqaghgYyCZAkAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPlE8L21pPjwvbWF0aD715aU4AAAAAElFTkSuQmCC" class="Wirisformula" alt="Q" width="13" height="14" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»Q«/mi»«/math»'/> as shown in figure about the point of projection is <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905357/1/914762/Picture528.png" alt="" width="166" height="122" />

Solution for the question - average torque on a projectile of mass 1 , initial speed u and angles ofprojection theta , between initial and final position p and