Two drones, Alpha and Beta, travel along straight-line paths in a horizontal surveying area.
Drone Alpha maintains a constant velocity of (9i+12j) m s−1(9\mathbf{i} + 12\mathbf{j}) \text{ m s}^{-1}(9i+12j) m s−1.
Drone Beta travels from the position vector (−5i+10j)(-5\mathbf{i} + 10\mathbf{j})(−5i+10j) metres to the position vector (22i+46j)(22\mathbf{i} + 46\mathbf{j})(22i+46j) metres over a duration of 6 seconds.
Show that the direction of motion of Beta is parallel to the direction of motion of Alpha.
A technician suggests that Beta must be moving with a constant velocity of (4.5i+6j) m s−1(4.5\mathbf{i} + 6\mathbf{j}) \text{ m s}^{-1}(4.5i+6j) m s−1. Explain why this statement might be false.
A third drone, Gamma, flies at a constant speed of 10 m s−110 \text{ m s}^{-1}10 m s−1 along a separate straight path. The flight paths of Alpha and Gamma intersect at a fixed waypoint XXX.
It is recorded that:
Demonstrate that the flight paths of Alpha and Gamma are perpendicular.
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.