Calculus
posted by Ali on .
Two ships leave the same port at noon. Ship A sails north at 22 mph, and ship B sails east at 12 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.)

after t hours, the distance d is given in terms of the distances x east and y north,
d^2 = x^2 + y^2
2d dd/dt = 2x dx/dt + 2y dy/dt
at 1:00, x=12 and y=22, so
d^2 = 12^2 + 22^2
d = 25
so,
2*25 dd/dt = 2(12)(12) + 2(22)(22)
dd/dt = 25.12 mi/hr 
QUESTION 3
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