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3.2 , motion in plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics3.2 , motion in plane1 Mark
MCQ
A mosquito is moving with a velocity $\overrightarrow{ v }=0.5 t ^{2} \hat{ i }+3 t \hat{ j }+9 \hat{ k }\, m / s$ 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
  • ✓
    $\tan ^{-1}\left(\frac{2}{3}\right)$ 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
✓

Answer

Correct option: B.
$\tan ^{-1}\left(\frac{2}{3}\right)$ from $y$ -axis
b
Given :

$\overrightarrow{ v }=0.5 t ^{2} \hat{ i }+3 t \hat{ j }+9 \hat{ k }$

$\overrightarrow{ v }_{ at\,t =2}=2 \hat{ i }+6 \hat{ j }+9 \hat{ k }$

$\therefore$ 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.

Hence this question should be bonus.

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