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Solution 19.8c

From Mechanics

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The expression for the position vector <math>\mathbf{r}</math> has been obtained in part b),
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The expression for the velocity <math>\mathbf{v}</math> has been obtained in part b).
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<math>\mathbf{v}=\left( 40 \right)\mathbf{i}+\left( -2t \right)\mathbf{j}</math>
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If the aeroplane is travelling south this is in the negative <math>\mathbf{j}</math> direction.
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If the aeroplane is travelling east this is in the positive <math>\mathbf{i}</math> direction.
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Thus if the aeroplane is travelling south east the <math>\mathbf{i}</math> component of the velocity must equal the minus <math>\mathbf{j}</math> component of the velocity.
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<math>\begin{align}
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& 40=-(-2t) \\
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& \\
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& t=20\text{ s} \\
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\end{align}</math>

Revision as of 17:06, 11 October 2010

The expression for the velocity v has been obtained in part b).

v=40i+−2tj 

If the aeroplane is travelling south this is in the negative j direction.

If the aeroplane is travelling east this is in the positive i direction.

Thus if the aeroplane is travelling south east the i component of the velocity must equal the minus j component of the velocity.

40=−(−2t)t=20 s

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