A mosquito is moving with a velocity v→=0.5t2 i∧+3t j∧+9 k∧m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2s?

A
$\tan^{- 1} (\frac{5}{2}) f r o m x - a x i s$
B
$\tan^{- 1} (\frac{2}{3})$ from x- axis
C
$\cos^{- 1} (\frac{6}{11}) f r o m y - a x i s$
D
$\tan^{- 1} (\frac{5}{2}) f r o m y - a x i s$

Solution:

$\begin{array}{l} \vec{v} = 0.5 t^{2} \hat{i} + 3 t \hat{j} + 9 \hat{k} \\ A t t = 2 s, \\ \vec{v} = 2 \hat{i} + 6 \hat{j} + 9 \hat{k} \\ |\vec{v}| = \sqrt{2^{2} + 6^{2} + 9^{2}} = 11 \\ H e n c e, \hat{v} = \frac{\vec{v}}{|\vec{v}|} = \frac{2}{11} \hat{i} + \frac{6}{11} \hat{j} + \frac{9}{11} \hat{k} \\ W i t h y a x i s, l e t s a y a n g l e m a d e i s β, \\ \cos β = \frac{6}{11} \\ \Rightarrow β = \cos^{- 1} (\frac{6}{11}) \end{array}$

Also Check:

A mosquito is moving with a velocity $\vec{v}$ =0.5 $t^{2}$ $\overset{\land}{i}$ +3t $\overset{\land}{j}$ +9 $\overset{\land}{k}$ m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2s?

Solution:

Related content

Company

Support

Courses

More

JEE

NEET

CBSE

NCERT solutions

NCERT exemplar

State Board

Subject

Rank Predictor

Engineering Entrance Exam

follow us