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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 A Answers

Skills

    1. (a) 2.02 s
    2. (b) 16.2 m
    1. (a) Horizontal 10.3 m s⁻¹, vertical 12.3 m s⁻¹
    2. (b) \(\mathbf{v} = \begin{pmatrix} 10.28 \\ 12.26 − 9.8t \end{pmatrix}\) m s⁻¹
    3. (c) \(\mathbf{r} = \begin{pmatrix} 10.28t \\ 12.26t − 4.9t^{2} \end{pmatrix}\) m
    1. (a) 1.03 s
    2. (b) 5.25 m
    3. (c) 45.0 m
    1. (a) 2.24 s
    2. (b) 63.1 m
    3. (c) 6.97 m
    1. (a) \(\mathbf{v} = \begin{pmatrix} 6 \\ −24.5 \end{pmatrix}\) m s⁻¹
    2. (b) 25.2 m s⁻¹
    3. (c) 76.2°
    1. (a) 1.89 s
    2. (b) 2.58 m
    3. (c) No, it hits the wall 1.92 m below the top

In context

    1. (a) 1.56 s
    2. (b) 4.69 m
    3. (c) 15.6 m s⁻¹, 78.9° below the horizontal
    1. (a) \(\mathbf{r} = \begin{pmatrix} 22.94t \\ 1.8 + 16.06t − 4.9t^{2} \end{pmatrix}\) m
    2. (b) 15.0 m
    3. (c) 3.39 s, 77.7 m
    1. (a) 3.02 m: clears by 1.12 m
    2. (b) 18.5 m s⁻¹
    3. (c) 31.3 m

Stretch

    1. (a) \(t = 0.459\) s and \(t = 2.67\) s
    2. (b) 5.90 m and 34.3 m
    3. (c) 2.21 s
    1. (a) Shown.
    2. (b) \(V = 15.7\) m s⁻¹

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