The position vectors of boats A A\,A and BBB, relative to a fixed origin OOO, are given by
RA=(12+9t)i+(−11−6t)j \mathbf R_A=(12+9t)\mathbf{i}+(-11-6t)\mathbf{j} RA=(12+9t)i+(−11−6t)jand
RB=(40−12t)i+(15t−39)j, \mathbf R_B=(40-12t)\mathbf{i}+(15t-39)\mathbf{j}, RB=(40−12t)i+(15t−39)j,where t t\,t is the number of hours after 6 a.m.
Find the initial position vectors and velocities of A A\,A and BBB.
Show that if both boats maintain their course and speed, they will collide and find the time and position vector at which this occurs.
At 7 a.m. boat A A\,A realises that a collision is imminent and changes course so that it now has velocity (−3i−15j)(-3\mathbf{i} - 15\mathbf{j})(−3i−15j) km h−1^{-1}−1. Find the distance between the two ships at the time when they would have collided.
363 exam-style questions on Edexcel A Level Maths Further Kinematics, covering 8.1 Vectors in Kinematics, 8.2 Vector Methods with Projectiles, 8.3 Variable Acceleration in One Dimension, 8.4 Differentiating Vectors, and 8.5 Integrating Vectors. Each one has a worked solution and a mark scheme showing where the marks go.