d
\({K_{max}} = \,\,hv - h{v_0}\,\,;\,\,\,{I_1} = \,\,4 \times \,\,{10^6}\,m\,/\sec \)

\(\frac{1}{2}m{v^2} = 2h{v_0} - h{v_0} = h{v_0}\)

\({K_{{{\max }_2}}} = 5h{v_0} - h{v_0} = 4h{v_0} = \frac{1}{2}mv_2^2\)

\(\frac{1}{2}mv_1^2 = h{v_0}\,\,\,\,\,\,.....(1)\,\,\,\,\,\,\frac{1}{2}mv_2^2 = 4h{v_0}\,\,\,\,\,\,\,\,\,......(2)\)

\((1)/(2) \Rightarrow \,\frac{{v_1^2}}{{v_2^2}} = \frac{1}{4}\)