A sailboat is being towed towards a 8'8′ high dock by means of a rope. Here r=r(t)r=r(t) represents the rope length at time tt. If the rate at which the rope length is changing(decreasing) is 55 feet/second , determine the speed at which the sailboat is approaching the dock when the rope length is r=10'r=10′.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.