Sol. $a_y=-400 \sqrt{3} \times 10^{10}\left[q \mathrm{E}_y=m a_y\right]$ $$ \begin{aligned} & R=5=\frac{40 \times 10^{12} \sin 2 \theta}{400 \sqrt{3} \times 10^{10}}\left[R(\text { range })=\frac{u^2 \sin 2 \theta}{a_y}\right] \\ & \sin 2 \theta=\frac{\sqrt{3}}{2} \\ & 2 \theta=60^{\circ}, 120 \Rightarrow \theta=30^{\circ}, 60^{\circ} \end{aligned} $$ Time of flight $\mathrm{T}_1=\frac{2 \times 2 \sqrt{10} \times 10^6 \times \frac{1}{2}}{400 \sqrt{3} \times 10^{10}}=\sqrt{\frac{5}{6}} \mu \mathrm{~s}\left(\right.$ for $\left.\theta=30^{\circ}\right)$ Time of flight $\mathrm{T}_2=\frac{2 \times 2 \sqrt{10} \times 10^6 \times \frac{\sqrt{3}}{2}}{400 \sqrt{3} \times 10^{10}}=\sqrt{\frac{5}{2}} \mu \mathrm{~s} \quad\left(\right.$ for $\left.\theta=60^{\circ}\right)$