Chapter 3 Test, problem 13

At noon, ship A is 200 km west of ship B. Ship A is sailing south at 34 km/hr and ship B is sailing north at 21 km/hr. How fast is the distance between the ships changing at 8:00 pm? Round the result to the nearest thousandth if necessary.

Step 1: Draw a picture and label all the parts.
The picture will be inserted on Tuesday...oh the mac fun.

Step 2: Find the static equation. Then plug in all constants.
(x^2) + (y^2) = (d^2)
(200^2) +(y^2) = (d^2)

Step 3: Find the information provided.
x = 200 km = constant
t = 8 hrs
y = (21 km/hr)(8 hrs) + (34 km/hr)(8 hrs) = 440 km
(d^2) = (200^2) + (440^2)
d = 483.3218 km
dy/dt = 34 km/hr - (-21 km/hr) = 55 km/hr

Step 4: Find the dynamic equation. Then plug in all known information.
0 + 2y(dy/dt) = 2d(dy/dt)
2(440 km)(55 km/hr) = 2(483.3218 km)(dd/dt)
dd/dt = 50.070 km/hr

Answer = 50.070 km/hr

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