Question

A boat sails 30 miles to the east from a point P, then it changes direction and sails to the south. If this boat is sailing at a constant speed of 10 miles/hr, at what rate is its distance from the point P increasing

a) 2 hours after it leaves the point P
b) 7 hours after it leaves the point P

Answer 1

The distance from point P after t hours is
d = sqrt[30^2 + (10 t)^2]
= sqrt(900 + 100 t^2)
dd/dt = [ (1/2)/( sqrt(900 + 100 t^2)]*200 t

Plug in the t value and compute the corresponding rate of change of d