Hướng dẫn giải

$\tan {{\alpha }_{1}}=\frac{{{v}_{01}}}{{{v}_{1}}}=\frac{{{v}_{01}}}{gt}$

$\tan {{\alpha }_{2}}=\frac{{{v}_{02}}}{{{v}_{2}}}=\frac{v2}{gt}$

${{\alpha }_{1}}+{{\alpha }_{2}}=90{}^\circ \Rightarrow \tan {{\alpha }_{1}}.\tan {{\alpha }_{2}}=1\Rightarrow {{v}_{01}}.{{v}_{02}}={{g}^{2}}{{t}^{2}}\Rightarrow t=\sqrt{\frac{{{v}_{01}}.{{v}_{02}}}{{{g}^{2}}}}=\frac{\sqrt{{{v}_{01}}.{{v}_{02}}}}{g}$