As observed from the top of a lighthouse, 72 m high above sea the angle of depression of a ship changes from 45° to 60° in 10 seconds. The speed (in m/s ) of the ship is -
Answer & explanation
Correct answer: option 2
in triangle ABD
tan 45° = \(\frac{AB}{BD}\)
1 = \(\frac{AB}{BD}\)
As , AB = 72 m . so , BD is also 72m
in triangle ABC
tan 60° = \(\frac{AB}{BC}\)
\(\sqrt{3}\) = \(\frac{AB}{BC}\)
\(\sqrt{3}\) = AB = 72 m
So , BC = \(\frac{72}{\sqrt{3}}\) = 24\(\sqrt{3}\)
The distance travelled by the ship = CD = BD - BC = 72 - 24\(\sqrt{3}\) =30.432 m
Distance = Speed × Time
Speed = \(\frac{30.432}{10}\) = 3.0432 m/s