QJEEM21Pha165: JEE Main 2021 Physics - Class 11 JEEM21Pha165 Solution: A mosquito is moving with a velocity v → = 0.5 t 2 i ^ + 3 t j…

Question

Verified Solution • 2025–26 Session moderate

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?

Accepted Answer

\vec{v} = (0.5 t^{2} \hat{i} + 3 t \hat{j} + 9 \hat{k})

m/s

At t = 2 s

\vec{v} = (2 \hat{i} + 6 \hat{j} + 9 \hat{k})

Direction cosine along y-axis,

c o s θ = \frac{(v . \hat{j})}{\sqrt{9^{2} + 6^{2} + 2^{2}}} = \frac{6}{\sqrt{121}} = \frac{6}{11}

∴

\sin θ = \frac{\sqrt{85}}{11}

and

\tan θ = \frac{\sqrt{85}}{6}

∴

Mosquito make angle

\tan^{- 1} (\frac{\sqrt{85}}{6})

from y-axis.

Step-by-Step Verified Solution