JEE PYQ: Motion In Two Dimensions Question 1
Question 1 - 2021 (16 Mar Shift 2)
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 2 s?
(a) $\tan^{-1}\left(\frac{2}{5}\right)$ from $x$-axis (b) $\tan^{-1}\left(\frac{\sqrt{85}}{6}\right)$ from $y$-axis (c) $\tan^{-1}\left(\frac{5}{2}\right)$ from $y$-axis (d) $\tan^{-1}\left(\frac{5}{2}\right)$ from $x$-axis
Show Answer
Answer: (b)
Solution
Given $\vec{v} = 0.5t^2\hat{i} + 3t\hat{j} + 9\hat{k}$. At $t = 2$: $\vec{v}_{t=2} = 2\hat{i} + 6\hat{j} + 9\hat{k}$. Angle from $y$-axis: $\cos^{-1}\frac{6}{11} = \tan^{-1}\frac{\sqrt{85}}{6}$.
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