An automated underwater vehicle (AUV) is moving through a calm lake at a constant velocity v=1.8i m s−1\mathbf{v} = 1.8\mathbf{i}\text{ m s}^{-1}v=1.8i m s−1. It is subject to exactly two constant horizontal forces: the drag from the water D=(−18.6i+24.5j) N\mathbf{D} = (-18.6\mathbf{i} + 24.5\mathbf{j})\text{ N}D=(−18.6i+24.5j) N and the propulsion thrust P=(αi−24.5j) N\mathbf{P} = (\alpha\mathbf{i} - 24.5\mathbf{j})\text{ N}P=(αi−24.5j) N.
Determine the value of α\alphaα.
Select your answer from the following:
−24.5-24.5−24.5
−18.6-18.6−18.6
18.618.618.6
24.524.524.5
87 exam-style questions on OCR (MEI) A Level Maths 3.4 Forces, covering 3.4.1 Language relating to forces, 3.4.2 Acceleration due to gravity, 3.4.3 Identify forces and draw force diagrams, 3.4.4 Resultant of concurrent forces, 3.4.5 Equilibrium of a particle, 3.4.6 Resolve a force into components (A-level only), 3.4.7 Equilibrium condition for resultant zero (A-level only), 3.4.8 Forces in equilibrium sum to zero (A-level only), 3.4.9 Equations for a particle in equilibrium (A-level only), 3.4.10 Frictional force and normal contact force (A-level only), 3.4.11 Model friction with F ≤ μR (A-level only), and 3.4.12 Apply Newton's Laws to friction problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.