A man is standing on the banks of a river, at distance of 36 m from a boat crossing the river. The angle of elevation from the position of the man to the boat changes from 30°`to 60° in 8 seconds . The speed (in m/s ) of the boat is -
Answer & explanation
Correct answer: option 3
in triangle ABC
tan 30° = \(\frac{BC}{AB}\)
\(\frac{1}{\sqrt{3}}\) = \(\frac{BC}{AB}\)
As , AB = 36 m . so , BC = \(\frac{36}{\sqrt{3}}\) = 12 \(\sqrt{3}\)
in triangle ABD
tan 60° = \(\frac{BD}{AB}\)
\(\sqrt{3}\) = \(\frac{BD}{AB}\)
AB = 36 m . So, BD = 36\(\sqrt{3}\) m
Distance covered by the boat = DC = DB - BC = 36\(\sqrt{3}\) - 12 \(\sqrt{3}\) = 24\(\sqrt{3}\) = 41.568
Distance = Speed × Time
Speed of the boat = \(\frac{41.568}{8}\) = 5.196 m/s