Solution 19.8d

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Current revision (17:57, 27 March 2011) (edit) (undo)
 
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The expression for the position vector <math>\mathbf{r}</math> has been obtained in part b).
The expression for the position vector <math>\mathbf{r}</math> has been obtained in part b).
-
<math>\mathbf{r}=\left( 40t \right)\mathbf{i}+\left( -2t+400 \right)\mathbf{j}</math>
+
<math>\mathbf{r}=\left( 40t \right)\mathbf{i}+\left( {-{t}^{2}}+400 \right)\mathbf{j}</math>
If the aeroplane is due east of the origin its position in the north-south direction must be zero, which means the <math>\mathbf{j}</math> component of the position vector must be zero.
If the aeroplane is due east of the origin its position in the north-south direction must be zero, which means the <math>\mathbf{j}</math> component of the position vector must be zero.
<math>\begin{align}
<math>\begin{align}
-
& -2t+400=0 \\
+
& {-{t}^{2}}+400=0 \\
& \\
& \\
-
& t=200\text{ s} \\
+
& t=20\text{ s} \\
\end{align}</math>
\end{align}</math>

Current revision

The expression for the position vector \displaystyle \mathbf{r} has been obtained in part b).

\displaystyle \mathbf{r}=\left( 40t \right)\mathbf{i}+\left( {-{t}^{2}}+400 \right)\mathbf{j}

If the aeroplane is due east of the origin its position in the north-south direction must be zero, which means the \displaystyle \mathbf{j} component of the position vector must be zero.

\displaystyle \begin{align} & {-{t}^{2}}+400=0 \\ & \\ & t=20\text{ s} \\ \end{align}

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