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  • The position of a particle is given by <img alt="\vec{r}=3t \hat{i}+2t^2\hat{j}+5\hat{k}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cvec%7Br%7D%3D3t%20%5Chat%7Bi%7D&plus;2t%5E

The position of a particle is given by \vec{r}=3t \hat{i}+2t^2\hat{j}+5\hat{k}

  where t is in seconds and the coefficients have a proper units for \vec{r} to be in meters. The direction of v(t) at t=1s is 

Option: 1

37\degree with the x-axis 


Option: 2

53\degree with the x-axis 


Option: 3

45\degree with the y-axis 


Option: 4

60\degree with the y-axis


Answers (1)

best_answer

\text{Given :}

\vec{r}=3t\hat{i}+2t^{2}\hat{j}+5\hat{k}

\vec{V}=\frac{d\vec{r}}{dt}=\frac{d}{dt}(3t \hat{i}+2t^2\hat{j}+5\hat{k})

\vec{V}=3\hat{i}+4t\hat{j} 

  \\ \text{At t= 1 sec},\\ \vec{v}=3\hat{i}+4\hat{j}

\\ \text{Let } \theta \text{ be the angle in which the direction of } \vec{v} \ \text{makes with the x-axis.}

\\ \text{Then,}

\\ tan\theta =\frac{v_{y}}{v_{x}}=\frac{4}{3}\\ \text{Or,} \\\theta =tan^{-1}\left ( \frac{4}{3} \right )=53^{\circ}

 

Posted by

Ritika Jonwal

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