Solution 8.10a
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(New page: We use, <math>\mathbf{r}=\mathbf{u}t+\frac{1}{2}\mathbf{a}{{t}^{\ 2}}+{{\mathbf{r}}_{0}}</math> to find an expression for the position of the aeroplane at a time t. Here, <math>{{\mathbf{...)
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Revision as of 16:25, 19 April 2010
We use, \displaystyle \mathbf{r}=\mathbf{u}t+\frac{1}{2}\mathbf{a}{{t}^{\ 2}}+{{\mathbf{r}}_{0}} to find an expression for the position of the aeroplane at a time t. Here,
\displaystyle {{\mathbf{r}}_{0}}=10\mathbf{k}\text{ m}
\displaystyle \mathbf{a}=(0\textrm{.}01\mathbf{i}+0\textrm{.}02\mathbf{j}+0\textrm{.}1\mathbf{k})\text{ m}{{\text{s}}^{\text{-2}}}
If a vector, like the starting velocity \displaystyle \mathbf{u} in this problem, points north east this means it has the same component in the east and north directions. In other words its \displaystyle \mathbf{i} component and its \displaystyle \mathbf{j} component are the same. Thus \displaystyle \mathbf{u} is of the form
\displaystyle \mathbf{u}=B\ \mathbf{i}+B \ \mathbf{ j}
This has magnitude \displaystyle \sqrt{{{B}^{2}}+{{B}^{2}}}=\sqrt{2}B
However the magnitude of the initial velocity is the initial sped which is
\displaystyle 8\sqrt{2}.
