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  • A man is moving with the velocity <img alt="\mathrm{\vec{v}=3 t^2 \hat{i}+5 t \hat{j}+9 \hat{k} }\; m/sec" src="/latex-image/?%5Cmathrm%7B%5Cvec%7Bv%7D%3D3%20t%5E2%20%5Chat%7Bi%7D&plus;5%2

A man is moving with the velocity \mathrm{\vec{v}=3 t^2 \hat{i}+5 t \hat{j}+9 \hat{k} }\; m/sec . and acceleration  in uniform motion. Find the direction of man after 2 sec with y-axis.

Option: 1

\mathrm{\tan ^{-1}\left(\frac{3}{2}\right)}


Option: 2

\mathrm{\tan ^{-1}\left(\frac{5}{2}\right)}


Option: 3

\mathrm{\tan ^{-1}\left(\frac{2}{3}\right)}


Option: 4

\mathrm{zero}


Answers (1)

best_answer

After t= 2 sec

   \mathrm{\vec{v}=12 \hat{\imath}+10 \hat{\jmath}+9 \hat{k}} 

angle with y-axis

\mathrm{\begin{aligned} \theta & =\tan ^{-1}\left(\frac{\sqrt{(12)^2+(9)^2}}{10}\right)\\ & =\tan ^{-1}\left(\frac{\sqrt{144+\theta 1}}{10}\right) \\ & =\tan ^{-1}\left(\frac{\sqrt{225}}{10}\right) \\ & =\tan ^{-1}\left(\frac{15}{10}\right) \\ & =\tan ^{-1}\left(\frac{3}{2}\right) \end{aligned}}

Posted by

Deependra Verma

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