Calculus - Related Rate 3
2013-12-01 10:03 pm
Two boats leave a port at the same time, one traveling west at 20 mi / hr and the other traveling south at 15 mi / hr. At what rate is the distance between them changing 30 minutes after they leave the port?
回答 (1)
2013-12-02 3:45 pm
✔ 最佳答案
Let location of the port be the origin. Let distance between the 2 boats be L.
So L^2 = x^2 + y^2 ( By Pythagoras thm.)
2L dLdt = 2x dx/dt + 2y dy/dt
L dL/dt = x dx/dt + y dy/dt.
dx/dt = 20
dy/dt = 15
After 30 min. ( 1/2 hr), x = 10, y = 7.5, L = sqrt ( 10^2 + 7.5^2) = 12.5
Rate of change of the distance between the 2 boats = dL/dt
= ( 10 x 20 + 15 x 7.5)/12.5 = 25 mi/hr.
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