to 1) The fishing boat needs
the ferry needs
So the ferry is 21 m south of the fishing boat when it reaches the point X. (Quite a narrow escape!)
to 2) Use the Pythagoran rule:
to 3) Use the Pythagoran rule. One leg is 400-8.5*t and the other is 120-3*t. So you get:
to 4) You are looking for the minimum distance. So d(t) has a minimum if D(t)=(d(t))² has a maximum. For convenience I use D(t)
. Thus t ≈ 46.3 s.
That means 0.7 s before the fishing boat arrives at point X the vessels are closest to each other.
d(46.3) ≈ 19.97 m ≈ 20 m
to 5) The visibility is 50 m. So the distance is less or equal 50 m.
. Solve for t. You'll get 2 values:
t_1 = 41.2 s or t_2 = 51.4 s
During these approximately 10 s they are visible to each other.