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IB Mathematics: Applications and Interpretation HL · AHL 4: Vectors · AHL 4.25

Projectiles: launch angle, launch height and clearing a wall Problem set B Answers

Skills

    1. (a) 0.495 s
    2. (b) 0.742 m
    1. (a) Horizontal 24.6 m s⁻¹, vertical 17.2 m s⁻¹
    2. (b) \(\mathbf{v} = \begin{pmatrix} 24.57 \\ 17.21 − 9.8t \end{pmatrix}\) m s⁻¹
    3. (c) \(\mathbf{r} = \begin{pmatrix} 24.57t \\ 17.21t − 4.9t^{2} \end{pmatrix}\) m
    1. (a) 0.972 s
    2. (b) 4.63 m
    3. (c) 10.7 m
    1. (a) 1.93 s
    2. (b) 19.0 m
    3. (c) 7.42 m
    1. (a) \(\mathbf{v} = \begin{pmatrix} 9 \\ −17.64 \end{pmatrix}\) m s⁻¹
    2. (b) 19.8 m s⁻¹
    3. (c) 63.0°
    1. (a) 1.60 s
    2. (b) 5.99 m
    3. (c) Yes, it clears the net by 0.787 m

In context

    1. (a) 1.28 s
    2. (b) 14.1 m
    3. (c) 16.7 m s⁻¹, 48.7° below the horizontal
    1. (a) \(\mathbf{r} = \begin{pmatrix} 10.24t \\ 2.1 + 8.004t − 4.9t^{2} \end{pmatrix}\) m
    2. (b) 5.37 m
    3. (c) 1.86 s, 19.1 m
    1. (a) 4.10 m: clears by 1.70 m
    2. (b) 14.4 m s⁻¹
    3. (c) 26.5 m

Stretch

    1. (a) \(t = 0.499\) s and \(t = 4.09\) s
    2. (b) 13.4 m and 110 m
    3. (c) 3.59 s
    1. (a) Shown.
    2. (b) \(V = 19.2\) m s⁻¹

jmaths.xyz · AI HL · AHL 4.25 Projectiles: launch angle, launch height and clearing a wall