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
130 exam-style questions on Edexcel A Level Maths Applications of Forces, covering 7.1 Static Particles, 7.2 Modelling with Statics, 7.3 Friction and Static Particles, 7.4 Static Rigid Bodies, 7.5 Dynamics and Inclined Planes, and 7.6 Connected Particles 2. Each one has a worked solution and a mark scheme showing where the marks go.