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IB Mathematics: Applications and Interpretation HL · AHL 4: Vectors · AHL 4.11
Constant velocity: speed, position and closest approach Problem set B Answers
Skills
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- (a) \(159^\circ\)
- (b) \(8.54\) m s\(^{-1}\)
- (c) \(310^\circ\)
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- (a) \(\begin{pmatrix} 6 \\ 9 \\ -18 \end{pmatrix}\)
- (b) \(\mathbf{v} = \frac{9}{\sqrt{30}}\begin{pmatrix} -2 \\ 5 \\ 1 \end{pmatrix} = \begin{pmatrix} -3.29 \\ 8.22 \\ 1.64 \end{pmatrix}\)
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- (a) \(\mathbf{r} = \begin{pmatrix} -5 \\ 1 \\ 8 \end{pmatrix} + t\begin{pmatrix} 2 \\ -3 \\ -1 \end{pmatrix}\)
- (b) \(9.49\) m
In context
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- (a) The equations give different values of \(t\), so no collision.
- (b) They collide when \(t = 2\) at \((-1, 6, 2)\)
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- (a) \(\overrightarrow{AB} = \begin{pmatrix} 9 - 3t \\ -9 + 2t \\ -4 + 2t \end{pmatrix}\)
- (b) \(t = 3.12\) minutes, distance 3.57 m
Stretch
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- (a) \(\begin{pmatrix} -2.62 \\ 5.24 \\ 1.31 \end{pmatrix}\)
- (b) \(\mathbf{r} = \begin{pmatrix} -20 \\ 35 \\ -5 \end{pmatrix} + t\begin{pmatrix} -2.62 \\ 5.24 \\ 1.31 \end{pmatrix}\)
- (c) \(129\) m
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- (a) The values of \(t\) differ, so no collision.
- (b) \(t = 2.67\) seconds, distance 4.90 m
- (c) Yes: the smallest distance, 4.90 m, is more than 3 m.
jmaths.xyz · AI HL · AHL 4.11 Constant velocity: speed, position and closest approach