Calculating how fast distance changes between ships

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At noon, ship A is 50 km west of ship B, with ship A sailing south at 30 km/h and ship B sailing north at 20 km/h. By 4:00 PM, ship A has traveled 120 km south, and ship B has traveled 80 km north, resulting in a total separation of 200 km in the north/south direction. The initial 50 km separation in the east/west direction remains unchanged. To find the overall distance between the ships, the Pythagorean theorem is applied, factoring in both the north/south and east/west distances. The discussion emphasizes the need to correctly apply the Pythagorean theorem to calculate the changing distance between the ships.
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Homework Statement



At noon, ship A is 50km west of ship B. Ship A is sailing south at 30km/h and ship B is sailing north at 20km/h. How fast is the distance between the ships changing at 4:00pm in km/h.

Homework Equations





The Attempt at a Solution



http://img822.imageshack.us/img822/2420/shipq2.png

but the final answer is coming out wrong
 
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I don't understand the very first line of your answer. Why are you taking the squares of the velocities? Where is the 50km in this? If you substitute t = 0 in your equation, what number should you get?
 
Ship A is heading south at 30 for 4 hours so travels 120 km. Similarly B travels 80 due north.
So they become separated by 200km north/south.
They are separated by 50 km due east west to begin with.

So the distance between the ships is? (pythagoras).
The angle of the same triangle is also the direction cosine of the motion so you can use that to calculate their mutual speed.
 

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