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An object falling freely covers half of its total distance in last second, then find total height and total times g = 9.8 ms^(-2).

Answer» <html><body><p></p>Solution :Suppose, total time is T and total height is h, <br/> In `h = ut + <a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>/2 <a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a> g ^(2) , u = 0` <br/> `h = 1/2g t ^(2) ""…(1)` <br/> Now `t = (T-1) and h = h/2` <br/> `h /2 = 1/2 g (T -1) ^(2)` <br/> `therefore h = g (T - 1) ^(2) ""…(2)` <br/> By comparing equation (1) and (2). <br/> `therefore 1/2 g t ^(2) = g (T ^(2) - 2T +1)` <br/> `therefore T ^(2) = 2 T ^(2) - 4 T + 2` <br/> `therefore T ^(2) -4T + 2=0` <br/> `a = 1, <a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a> =- 4, c =2` <br/> `Delta = b ^(2) - 4ac` <br/> `=<a href="https://interviewquestions.tuteehub.com/tag/16-276476" style="font-weight:bold;" target="_blank" title="Click to know more about 16">16</a>-4 xx 1 xx 2 ` <br/>`=16 -8 =8` <br/> `therefore sqrtDelta = 2 <a href="https://interviewquestions.tuteehub.com/tag/sqrt2-3056932" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT2">SQRT2</a>` <br/> `therefore` Solution `T = (-b pm sqrtDelta )/( 2a) = (4 pm 2 sqrt2)/(2)` <br/> `T = 2 pm sqrt2` <br/> `therefore T = 2 + 1.4.4 = 3.414s or 2-1414 = 0.586 s` <br/> But `T=0.586` s is not possible <br/> `therefore T = 3.414 s ` <br/> Now from equation `h = 1/2 g t ^(2) ` <br/> `h = 1/2 xx 9.8 xx (3.414) ^(2)` <br/> `therefore h = 57.11 m`</body></html>


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