jarp0120
  • jarp0120
please help a ship is sailing north at 22 km/hr. a second ship sailing east at 16 km/hr crosses the path of the first ship 85 km ahead of it. how fast is the distance between them changing 1 hour later? when are they closes together?
Mathematics
katieb
  • katieb
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phi
  • phi
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phi
  • phi
\[ c^2 = x^2 + y^2 \] take the derivative with respect to time \[ 2 c \ \dot{c} = 2x \ \dot{x} + 2y \ \dot{y}\] and solve for c dot (= dc/dt)
phi
  • phi
In general, the y value (of the ship moving north) is (85-22t) the x value of the east going ship is 16t \[ c^2 = (85-22t)^2 + 256t^2 \] take the derivative with respect to t \[ 2 c \ \dot{c} = 2(85-22t)(-22) + 2\cdot 256 t \\ \dot{c} = \frac{-22(85-22t)+ 256 t }{c} \] set dc/dt to zero to find the min value \[ \frac{-22(85-22t)+ 256 t }{c} =0 \\ -22(85-22t)+ 256 t=0 \] solve for t (in hours)

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jarp0120
  • jarp0120
t is 187/74 hr?
phi
  • phi
yes, that looks good
jarp0120
  • jarp0120
@phi thank you for your help

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