Homework SourseAt 100 pm ship A is 25 miles due south of ship B If ship A i
At 1:00 pm, ship A is 25 miles due south of ship B. If ship A is sailing west at the rate of 16 miles/hour and ship B is sailing south at a rate of 20 miles/hour, find the rate at which the distance between the ships is changing at 1:30 pm.
Solution
Let the North-South direction be the Y axis direction and the east west direction be the x direction. Let ship A be at point (0,0) and ship B be at (0,25). The distance is determined by d = sqrt((x1-x2)^2 + (y1-y2)^2) [DISTANCE FORMULA] If we let ship A be determine (x1,y1) and ship B determine (x2,y2), then (by writing the positions of A and B as functions of the parameter t) x2=0, y1=0, x1 = -16t, and y2 = 25 - 20t. Substiute with time values and differentiate d(t) = sqrt((-16t)^2 + (25 - 20t)^2) = sqrt(416t^2 - 100t +625) d`(t)= (4*(104t - 125))/(sqrt(416t^2 - 100t +625)) d`(30) = 2396/sqrt(13801) = 20.4 mi/hr
