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Question

For maximum range $	heta=45^{\circ}$ $\mathrm{R}=100 \mathrm{km}=10^{5} \mathrm{m}(	ext { maximum })$

$\mathrm{R}=\frac{\mathrm{u}^{2}}{\mathrm{g

Vedclass · Accepted Answer

$\frac{{100}}{{\sqrt 2 }}\,s$

Vedclass · Answer

For maximum range $	heta=45^{\circ}$ $\mathrm{R}=100 \mathrm{km}=10^{5} \mathrm{m}(	ext { maximum })$

$\mathrm{R}=\frac{\mathrm{u}^{2}}{\mathrm{g}} \quad\left(\because 	heta=45^{\circ}, \quad 	herefore \sin 2 	heta=1ight)$

$\Rightarrow \mathrm{u}^{2}=\mathrm{g} \mathrm{R} \Rightarrow \mathrm{u}=\sqrt{\mathrm{gR}}$

Time of flight $\mathrm{T}=\frac{2 \mathrm{u} \sin 	heta}{\mathrm{g}}$

After top point, time remaining $\mathrm{t}=\frac{\mathrm{T}}{2}$

$\Rightarrow \mathrm{t}=\frac{\mathrm{u} \sin 45^{\circ}}{\mathrm{g}}$

$=\frac{\sqrt{\mathrm{gR}}}{\mathrm{g}} 	imes \frac{1}{\sqrt{2}}$

$=\sqrt{\frac{\mathrm{R}}{\mathrm{g}}} \cdot \frac{1}{\sqrt{2}}=\sqrt{\frac{10^{5}}{10}} 	imes \frac{1}{\sqrt{2}}$

$=\frac{100}{\sqrt{2}} \mathrm{s}$

A missile is fired for maximum range at your town from a place $100\, km$ away from you. If the missile is first detected at its half way point, how much warning time will you have ? (Take $g = 10\, m/s^2$)

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