At 10 a.m. a plane A A\,A has position vector (2i−5j)(2\mathbf{i} - 5\mathbf{j})(2i−5j) km and moves with constant velocity (−4i+6j)(-4\mathbf{i} + 6\mathbf{j})(−4i+6j) km h−1^{-1}−1.
At the same time a plane B B\,B has position vector (−3i−9j)(-3\mathbf{i} - 9\mathbf{j})(−3i−9j) km and moves with constant velocity (i+8j)(\mathbf{i} + 8\mathbf{j})(i+8j) km h−1^{-1}−1.
The unit vectors i\mathbf{i}i and j\mathbf{j}j are due east and due north respectively.
Find the position vector of A A\,A relative to B B\,B at t t\,t hours after 10 a.m.
Find the time at which A A\,A is due west of BBB.
Find the time, after 10 a.m., at which the planes are exactly 37 km apart.
158 exam-style questions on OCR (MEI) A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Position, displacement, distance and distance travelled, 3.2.3 Velocity, speed and acceleration distinctions, 3.2.4 Draw and interpret kinematics graphs, 3.2.5 Differentiate position and velocity (A-level only), 3.2.6 Integrate acceleration and velocity (A-level only), 3.2.7 When constant acceleration formulae apply, 3.2.8 Solve 1-D kinematics problems, 3.2.9 Language of kinematics in 2 dimensions (A-level only), 3.2.10 Extend 1-D techniques to 2-D using vectors (A-level only), 3.2.11 Cartesian equation of a path (A-level only), and 3.2.12 Vectors to solve kinematics problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.