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Homework Statement
There are two ships separated by a distance [tex]\gamma[/tex] along a straight coastline. Ship A starts moving perpendicularly to the coastline , and Ship B moves such that its velocity vector always point along the position of Ship A.
Both ships move at same constant speed. After sufficient time, both the ships will move in a straight line with a constant separation. Find this separation.
2. MY ATTEMPT
First, i assumed the constant speed to be v
and let, after time T, both of them move in a straight line.
and let [tex]\theta[/tex] be the angle that the velocity vector of ship B makes with that of the other. ([tex]\theta[/tex] is variable from [itex]\pi / 2 \ \rightarrow \ 0 [/itex] ) . I feel [itex]tan\theta \ = \ \frac{\gamma}{vt}[/itex]
Then [tex]\gamma \ = \ v \ sin \theta \times T [/tex]
and [tex]x \ = \ T (v-vcos \theta) [/tex]
x= constant separation when ships are in a straight line
The problem is, I am unable to get differential equations which i should. How do i convert the known data into differential form ?
Any help is appreciated
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