A mosquito is moving with a velocity $\overrightarrow v = 0.5{t^2}\widehat i + 3t\widehat j + 9\widehat k$ m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2 s?
Solution
$\overrightarrow v = (0.5{t^2}\widehat i + 3t\widehat j + 9\widehat k)$ m/s<br><br>At t = 2 s<br><br>$\overrightarrow v = (2\widehat i + 6\widehat j + 9\widehat k)$
<br><br>Direction cosine along y-axis,
<br><br>$$cos\theta = {{(v.\widehat j)} \over {\sqrt {{9^2} + {6^2} + {2^2}} }} = {6 \over {\sqrt {121} }} = {6 \over {11}}$$<br><br>$\therefore$ $\sin \theta = {{\sqrt {85} } \over {11}}$<br><br>and $\tan \theta = {{\sqrt {85} } \over 6}$
<br><br>$\therefore$ Mosquito make angle ${\tan ^{ - 1}}\left( {{\sqrt {85} } \over 6}\right)$ from y-axis.
About this question
Subject: Physics · Chapter: Kinematics · Topic: Motion in a Straight Line
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