Question Number 17999 by Tinkutara last updated on 13/Jul/17
$$\mathrm{A}\:\mathrm{large}\:\mathrm{number}\:\mathrm{of}\:\mathrm{bullets}\:\mathrm{are}\:\mathrm{fired}\:\mathrm{in} \\ $$$$\mathrm{all}\:\mathrm{direction}\:\mathrm{with}\:\mathrm{same}\:\mathrm{speed}\:{u}.\:\mathrm{The} \\ $$$$\mathrm{maximum}\:\mathrm{area}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{covered} \\ $$$$\mathrm{by}\:\mathrm{these}\:\mathrm{bullets}\:\mathrm{will}\:\mathrm{be} \\ $$$$\left(\mathrm{1}\right)\:\pi.\frac{{u}^{\mathrm{2}} }{{g}} \\ $$$$\left(\mathrm{2}\right)\:\pi.\frac{{u}^{\mathrm{4}} }{{g}^{\mathrm{2}} } \\ $$$$\left(\mathrm{3}\right)\:\frac{\pi}{\mathrm{4}}.\frac{{u}^{\mathrm{4}} }{{g}^{\mathrm{2}} } \\ $$$$\left(\mathrm{4}\right)\:\frac{\pi}{\mathrm{2}}.\frac{{u}^{\mathrm{4}} }{{g}^{\mathrm{2}} } \\ $$
Answered by ajfour last updated on 13/Jul/17
$$\mathrm{Range}\:\mathrm{is}\:\mathrm{then}\:\mathrm{a}\:\mathrm{maximum},\:\mathrm{R}=\frac{\mathrm{u}^{\mathrm{2}} }{\mathrm{g}} \\ $$$$\mathrm{Area}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{R}. \\ $$$$\mathrm{So}\:\:\mathrm{Area}\:\mathrm{A}=\pi\mathrm{R}^{\mathrm{2}} =\pi.\frac{\mathrm{u}^{\mathrm{4}} }{\mathrm{g}^{\mathrm{2}} }\:\:;\:\mathrm{option}\:\left(\mathrm{2}\right). \\ $$
Commented by Tinkutara last updated on 14/Jul/17
$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$