Kinematics with constant velocity Problem set B Answers

1. (a) 69°
2. (b) 140°

1. (a) √157 = 12.5 m s⁻¹
2. (b) 11 m s⁻¹
3. (c) √69 = 8.31 m s⁻¹

1. (a) \(\begin{pmatrix}40\\42\end{pmatrix}\) m s⁻¹
2. (b) \(8\mathbf{i} + 8\mathbf{j} + 14\mathbf{k}\) m s⁻¹
3. (c) \(\mathbf{r} = \begin{pmatrix}5\\-2\\1\end{pmatrix} + t\begin{pmatrix}6\\12\\4\end{pmatrix}\)

1. (a) √16.25 = 4.03 m s⁻¹
2. (b) \(\mathbf{r} = (7\mathbf{i} - \mathbf{j} - 4\mathbf{k}) + t(-\mathbf{i} + 3\mathbf{j} + 2.5\mathbf{k})\)
3. (c) No: the components give different values of t

1. (a) (1, −5, 2)
2. (b) 6 m s⁻¹
3. (c) 17.1 m

5.10 m

1. (a) \(\mathbf{r}_R = (9 - 3t)\mathbf{i} + (-2 + 4t)\mathbf{j},\quad \mathbf{r}_S = (-6 + 2t)\mathbf{i} + (10 - t)\mathbf{j}\)
2. (b) 5.39 km
3. (c) t = 3 hours

1. (a) They cross at (−4, 6, 3)
2. (b) The first object is at (−4, 6, 3) when t = 2 and the second when t = 4: different times

1. (a) 7 m s⁻¹ and 5 m s⁻¹
2. (b) They meet at t = 2 at (5, 1, 4)

1. (a) Shown
2. (b) 2.68 km
3. (c) t = 3

1. (a) They collide at t = 3 at (3, 2, 13)
2. (b) 1.41 m

1. (a) t = 3
2. (b) 1.6 m

1. (a) c = 2
2. (b) 17.6 km h⁻¹