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Question-67215




Question Number 67215 by Learner-123 last updated on 24/Aug/19
Commented by Learner-123 last updated on 24/Aug/19
  help me in Q.74.
$$\:\:{help}\:{me}\:{in}\:{Q}.\mathrm{74}. \\ $$
Answered by mr W last updated on 24/Aug/19
h=4m  s_1 =h+0.75h=1.75h  s_2 =0.75h+0.75^2 h=0.75×1.75h  ....  s=Σ_(n=1) ^∞ s_n =((1.75h)/(1−0.75))=7h=7×4=28m    t_1 =(√(h/(4.9)))+(√((0.75h)/(4.9)))=(1+(√(0.75)))(√(h/(4.9)))  t_2 =(√((0.75h)/(4.9)))+(√((0.75^2 h)/(4.9)))=(√(0.75))(1+(√(0.75)))(√(h/(4.9)))  ...  t=Σ_(n=1) ^∞ t_n =((1+(√(0.75)))/(1−(√(0.75))))×(√(h/(4.9)))=12.58 sec
$${h}=\mathrm{4}{m} \\ $$$${s}_{\mathrm{1}} ={h}+\mathrm{0}.\mathrm{75}{h}=\mathrm{1}.\mathrm{75}{h} \\ $$$${s}_{\mathrm{2}} =\mathrm{0}.\mathrm{75}{h}+\mathrm{0}.\mathrm{75}^{\mathrm{2}} {h}=\mathrm{0}.\mathrm{75}×\mathrm{1}.\mathrm{75}{h} \\ $$$$…. \\ $$$${s}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{s}_{{n}} =\frac{\mathrm{1}.\mathrm{75}{h}}{\mathrm{1}−\mathrm{0}.\mathrm{75}}=\mathrm{7}{h}=\mathrm{7}×\mathrm{4}=\mathrm{28}{m} \\ $$$$ \\ $$$${t}_{\mathrm{1}} =\sqrt{\frac{{h}}{\mathrm{4}.\mathrm{9}}}+\sqrt{\frac{\mathrm{0}.\mathrm{75}{h}}{\mathrm{4}.\mathrm{9}}}=\left(\mathrm{1}+\sqrt{\mathrm{0}.\mathrm{75}}\right)\sqrt{\frac{{h}}{\mathrm{4}.\mathrm{9}}} \\ $$$${t}_{\mathrm{2}} =\sqrt{\frac{\mathrm{0}.\mathrm{75}{h}}{\mathrm{4}.\mathrm{9}}}+\sqrt{\frac{\mathrm{0}.\mathrm{75}^{\mathrm{2}} {h}}{\mathrm{4}.\mathrm{9}}}=\sqrt{\mathrm{0}.\mathrm{75}}\left(\mathrm{1}+\sqrt{\mathrm{0}.\mathrm{75}}\right)\sqrt{\frac{{h}}{\mathrm{4}.\mathrm{9}}} \\ $$$$… \\ $$$${t}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{t}_{{n}} =\frac{\mathrm{1}+\sqrt{\mathrm{0}.\mathrm{75}}}{\mathrm{1}−\sqrt{\mathrm{0}.\mathrm{75}}}×\sqrt{\frac{{h}}{\mathrm{4}.\mathrm{9}}}=\mathrm{12}.\mathrm{58}\:{sec} \\ $$
Commented by Learner-123 last updated on 24/Aug/19
thanks sir.
$${thanks}\:{sir}. \\ $$

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