Hi,

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.

EB