A marine salvage ROV (Remotely Operated Vehicle) of mass 2.5 kg is operating at depth. Its motion is governed by two horizontal thruster forces P1\mathbf{P}_1P1 and P2\mathbf{P}_2P2 such that:
P1=(3a−11) N and P2=(52b) N \mathbf{P}_1 = \begin{pmatrix} 3a \\ -11 \end{pmatrix} \text{ N and } \mathbf{P}_2 = \begin{pmatrix} 5 \\ 2b \end{pmatrix} \text{ N} P1=(3a−11) N and P2=(52b) Nwhere a a\,a and b b\,b are constant parameters. The resulting acceleration of the ROV is observed to be a=(2ba−1) m s−2\mathbf{a} = \begin{pmatrix} 2b \\ a - 1 \end{pmatrix} \text{ m s}^{-2}a=(2ba−1) m s−2.
Determine the value of a a\,a and the value of bbb.
197 exam-style questions on OCR A Level Maths 1.10 Vectors, covering 1.10.1 Vectors in two dimensions, 1.10.2 Vectors in three dimensions (A-level only), 1.10.3 Magnitude and direction of vectors, 1.10.4 Basic operations on vectors, 1.10.5 Position vectors, 1.10.6 Distance between points, 1.10.7 Problem solving using vectors, 1.10.8 Vectors in kinematics, and 1.10 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.