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 :
[tex]s^2=9^2+d^2[/tex]
[tex]s^2=81+d^2[/tex]
[tex]s=\sqrt{81+d^2}[/tex]
or [tex]f(d)=\sqrt{81+d^2}[/tex]
(b) Let g(t) is the function at t = 0 and at 12 pm.
[tex]f(g)=fog[/tex]
Since, distance, d = 25t
So, [tex]f(g(t))=\sqrt{9^2+(25t)^2}[/tex]
[tex]f(g(t))=\sqrt{81+(652t)^2}[/tex]
Hence, this is the required solution.
