Question 2. Deep sea drones are used to explore the bottom of the ocean. The drone...
Question 2. Deep sea drones are used to explore the bottom of the ocean. The drone is allowed to sink using its weight force, however if the drone hits the ocean floor with a high velocity the operational camera will break. Hence the velocity of the sinking drone should be less than 4 m/s when hitting the ocean floor. The weight force is countered by drag and buoyancy (See Figure 1). Drag is directly proportional to velocity i.e. D = av for some constant a (this is experimentally confirmed for velocities that are not too large). Sea level y = 0 Drag = av Buoyancy = weight of displaced fluid Weight = mass of drone x gravity Using Newton's second law, construct a first order ordinary differential equation describing the vertical velocity of the drone. Hence find expressions for v(t) and y(t) in terms of buoyancy, weight and some constant a. Assume that the drone is initially at rest and that its journey starts at sea level. [9] Consider a drone that has a density of 1.3 kg/m3 and a volume of 1.2 m3 and that a was experimentally determined to be 0.6 kg/s. Determine the depth limit for the drone. [5] Using mathematical reasoning explain how you could design a drone that was able to explore oceans of any depth with the same camera.