Randall D. Knight — Dynamics I: Motion Along a Line: Problem 64

An oceanographic research ship uses a cable to tow a submerged sonar system that maps the ocean floor. The submersible travels horizontally because the vertical component of the cable tension and an upward buoyant force from the water balance the gravitational force. One submersible has a cross-section area of $1.3\text{ m}^2$ and a drag coefficient of $0.85$. The tow cable makes a $30^\circ$ angle with the horizontal when pulling the submersible at $5.1\text{ m/s}$. What is the magnitude of the tension in the cable? The density of seawater is $1020\text{ kg/m}^3$.