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
5 exam-style questions on OCR A Level Maths 3.3.14 Equilibrium of forces in two dimensions using vectors (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.