Kinematics

JEE Main level, single correct, medium

33 of 308

Question 33 of 308

A mosquito is moving with a velocity v⃗=0.5t2i^+3tj^+9k^ms−1\vec{v}=0.5{t}^{2}\hat{i}+3t\hat{j}+9\hat{k}m{s}^{-1} and accelerating in uniform conditions. What will be the direction of mosquitoes after 2s2s ?

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Answer: (B) tan⁡−1(856){\tan }^{-1}\left(\dfrac{\sqrt{85}}{6}\right) from yy-axis

Given :
v⃗=0.5t2i^+3tj^+9k^\vec{v}=0.5{t}^{2}\hat{i}+3t\hat{j}+9\hat{k}
v⃗att=2=2i^+6j^+9k^{\vec{v}}_{att=2}=2\hat{i}+6\hat{j}+9\hat{k}
∴∴ Angle made by direction of motion of mosquito will be,
cos⁡−1211{\cos }^{-1}\dfrac{2}{11} (from xx-axis) =tan⁡−11172={\tan }^{-1}\dfrac{\sqrt{117}}{2}
cos⁡−1611{\cos }^{-1}\dfrac{6}{11} (from yy-axis) =tan⁡−1856={\tan }^{-1}\dfrac{\sqrt{85}}{6}
cos⁡−1911{\cos }^{-1}\dfrac{9}{11} (from zz-axis) =tan⁡−1409={\tan }^{-1}\dfrac{\sqrt{40}}{9}

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