Homework Help Forum: calculus

Posted by Ash on Thursday, October 29, 2009 at 5:38pm.

At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 23 knots. How fast (in knots) is the distance between the ships changing at 3 PM?

• calculus - Reiny, Thursday, October 29, 2009 at 6:36pm

  Let the distance between them be D n miles. Let the time passes since noon be t hours. Did you make a diagram? I see a right-angles triangle with sides (23t), (17t + 30) and D so that D^2 = (23t)^2 + (17t + 30)^2 2D(dD/dt) = 2(23t)(23) + 2(17t+30)(17) dD/dt = (529t + 289t + 510)/D when t = 3, (3:00 pm) D^2 = 4761+6561 D = 106.405 dD/dt = (529(3) + 289(3) +510)/106.405 = 27.86 knots

  
  

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