Answer:
The speed of the boat is approximately 0.704 m/s
Step-by-step explanation:
The time it takes the man in the boat to change the angle of elevation from 60° to 45°, t = 2 minutes = 120 seconds
The height of the light house = 200 m
Given that the angle of elevation is reducing, the direction of the man is away from the lighthouse
The initial distance of the man in the boat from the lighthouse = 200 m/(tan(60°)) = (200/√3) m
The final distance of the man in the boat from the lighthouse = 200 m/(tan(45°)) = 200 m
The distance traveled in 2 minutes, d = 200 m - (200/√3) m ≈ 84.53 m
The speed of the boat, v = d/t
∴ v = 84.53 m/(2 min × 60 s/min) ≈ 0.704 m/s
The speed of the boat, v ≈ 0.704 m/s.
