jmaths
IB Mathematics: Applications and Interpretation HL · AHL 4: Vectors · AHL 4.11
Constant velocity: speed, position and closest approach Problem set A Answers
Skills
-
- (a) \(113^\circ\)
- (b) \(7.62\) m s\(^{-1}\)
- (c) \(309^\circ\)
-
- (a) \(\begin{pmatrix} 5 \\ -10 \\ 10 \end{pmatrix}\)
- (b) \(\mathbf{v} = \frac{12}{\sqrt{38}}\begin{pmatrix} 2 \\ 3 \\ 5 \end{pmatrix} = \begin{pmatrix} 3.89 \\ 5.84 \\ 9.73 \end{pmatrix}\)
-
- (a) \(\mathbf{r} = (6\mathbf{i} - 4\mathbf{j} + 2\mathbf{k}) + t(-\mathbf{i} + 3\mathbf{j} + 2\mathbf{k})\)
- (b) \(13.0\) m
In context
-
- (a) The equations give different values of \(t\), so no collision.
- (b) They collide when \(t = 3\) at \((5, 2, 7)\)
-
- (a) \(\overrightarrow{AB} = \begin{pmatrix} -7 + t \\ 4 - t \\ -3 + t \end{pmatrix}\)
- (b) \(t = 4.67\) hours, distance 2.94 km
Stretch
-
- (a) \(\begin{pmatrix} 7.10 \\ -2.37 \\ 11.8 \end{pmatrix}\)
- (b) \(\mathbf{r} = \begin{pmatrix} 40 \\ 25 \\ 10 \end{pmatrix} + t\begin{pmatrix} 7.10 \\ -2.37 \\ 11.8 \end{pmatrix}\)
- (c) \(307\) m
-
- (a) The values of \(t\) differ, so no collision.
- (b) \(t = 2.47\) hours, distance 2.18 km
- (c) No: the smallest distance, 2.18 km, is less than 2.5 km.
jmaths.xyz · AI HL · AHL 4.11 Constant velocity: speed, position and closest approach