Question

A mosquito is moving with a velocity $\vec{v}=0.5t^2\hat{i}+3t\hat{j}+9\hat{k}m/s$ and accelerating in uniform conditions. What will be the direction of mosquito after $2s$ ?

• A. ${\tan }^{-1}\left(\frac{2}{3}\right)$ from $x$ -axis
• B. ${\tan }^{-1}\left(\frac{2}{3}\right)$ from $y$ -axis
• C. ${\tan }^{-1}\left(\frac{5}{2}\right)$ from $y$ -axis
• D. none of the above

Answer 1

Answer: (D)

Given:
$\vec{v}=0.5t^2\hat{i}+3t\hat{j}+9\hat{k}$
${\vec{v}}_{\text{at}t=2}=2\hat{i}+6\hat{j}+9\hat{k}$
$\therefore$ 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.