Answer Number 6 6. A particle moves so that its position vector is given by $\vec{r} = \sin 5t \, \hat{i} - \cos 5t \, \hat{j}$, where $t$ is the time. Find the angle between the velocity $\vec{V}$ of the particle and the position vector $\vec{r}$.

Name: Answer Number 6 6. A particle moves so that its position vector is giv
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Description: Answer Number 6 6. A particle moves so that its position vector is given by $\vec{r} = \sin 5t \, \hat{i} - \cos 5t \, \hat{j}$, where $t$ is the time. Find the angle between the velocity $\vec{V}$ of the particle and the position vector \(\vec

Consider the given position vector. r→=sin5ti⌢−cos5tj⌢ Now, calculate the velocity vector of the…

Answered: 6. A particle moves so that its…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Answer Number 6

6. A particle moves so that its position vector is given by $\vec{r} = \sin 5t \, \hat{i} - \cos 5t \, \hat{j}$, where $t$ is the time. Find the angle between the velocity $\vec{V}$ of the particle and the position vector $\vec{r}$.

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Step 1

Consider the given position vector.

$\vec{r} = \sin 5 t \overset{⌢}{i} - \cos 5 t \overset{⌢}{j}$

Now, calculate the velocity vector of the particle.

$\begin{array}{rcl} \vec{\frac{d r}{d t}} & = & \frac{d}{d t} [\sin 5 t \overset{⌢}{i} - \cos 5 t \overset{⌢}{j}] \\ \vec{V} & = & 5 \cos t 5 t \overset{⌢}{i} + 5 \sin 5 t \overset{⌢}{j} \end{array}$

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