Question

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

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