Refer to the diagram shown below.
Let the ship approach the lighthouse at a constant speed of v km/h.
When the angle of elevation is 0.005 radians,
tan(0.005) = 30/(x + y)
x + y = 30/tan(0.005) = 6000 m (1)
When the angle of elevation is 0.1 radian,
tan(0.1) = 30/x
x = 30/tan(0.1) = 299 m
From (1), obtain
y = 6000 - 299 = 5701 m = 5.701 km
The ship travels 5701 m in 10 minutes. It's speed is
v = (5.701 km)/(1/6 h) = 34.2 km/h
Answer: The ship is traveling at 34.2 km/h.
