Aship is moving at a speed of 25 km/h parallel to a straight shoreline. the ship is 9 km from shore and it passes a lighthouse at noon. (a) express the distance s between the lighthouse and the ship as a function of d, the distance the ship has traveled since noon. s = f(d) = (b) express d as a function of t, the time elapsed since noon. d = g(t) = (c) find f ∘ g. (f ∘ g)(t) =

Explanation:

It is given that,

Speed of the ship, v = 25 km/h

Distance between the ship and the shore is 9 km

Let s is the distance between the lighthouse and the ship and d is the distance traveled by the ship since noon.

(a) Using Pythagoras theorem in the attached diagram as :

or

(b) Let g(t) is the function at t = 0 and at 12 pm.

Since, distance, d = 25t

So,

Hence, this is the required solution.

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