A high-precision calibration glider of mass 0.4 kg is being manipulated on a horizontal low-friction air-table. Two magnetic actuators exert forces F1\mathbf{F}_1F1 and F2\mathbf{F}_2F2 on the glider, where:
F1=[2a1.8] N and F2=[−3b] N \mathbf{F}_1 = \begin{bmatrix} 2a \\ 1.8 \end{bmatrix} \text{ N and } \mathbf{F}_2 = \begin{bmatrix} -3 \\ b \end{bmatrix} \text{ N} F1=[2a1.8] N and F2=[−3b] Nand a,b a, b\,a,b are constants. The glider's resulting acceleration vector is given by a=[5b10a] m s−2\mathbf{a} = \begin{bmatrix} 5b \\ 10a \end{bmatrix} \text{ m s}^{-2}a=[5b10a] m s−2.
Determine the value of a a\,a and the value of bbb.
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.