A mosquito is moving with a velocity $\overrightarrow{\mathrm{v}}=0.5 \mathrm{t}^{2} \hat{\mathrm{i}}+3 \mathrm{t} \hat{\mathrm{j}}+9 \hat{\mathrm{k}}$ m/s and accelerating in uniform conditions. What will be the direction of mosquito after $2 \mathrm{~s}$ ?
Correct Option: , 2
Given :
$\overrightarrow{\mathrm{v}}=0.5 \mathrm{t}^{2} \hat{\mathrm{i}}+3 \mathrm{t} \hat{\mathrm{j}}+9 \hat{\mathrm{k}}$
$\overrightarrow{\mathrm{v}}_{\mathrm{at} t=2}=2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+9 \hat{\mathrm{k}}$
$\therefore$ Angle made by direction of motion of mosquito will be,
$\cos ^{-1} \frac{2}{11}($ from x-axis $)=\tan ^{-1} \frac{\sqrt{117}}{2}$
$\cos ^{-1} \frac{6}{11}$ (from y-axis) $=\tan ^{-1} \frac{\sqrt{85}}{6}$
$\cos ^{-1} \frac{9}{11}$ (from z-axis) $=\tan ^{-1} \frac{\sqrt{40}}{9}$
None of the option is matching.
Hence this question should be bonus.