(Full score for this small question 10) There is a mountain peak with an altitude of 1km on the island, and there is an observation station at the top of the mountain. There is a ship traveling at a c

(Full score for this small question 10) There is a mountain peak with an altitude of 1km on the island, and there is an observation station at the top of the mountain. There is a ship traveling at a constant speed in a fixed direction. ( 1) ; (2)

Solution: (1) Let the ship speed be km/h, then km.

In δ, ∠ is equal to the depression angle of 30, ∴.

Similarly, Delta. ? (4 points)

In delta ≈ 15+45 = 60,

∴ From cosine theorem,

∴ km/h, the speed of the ship is km/h (6 minutes).

(2) (Method 1) Do it at the point. When the ship reaches the point, it is the smallest, so it is the smallest.

At this point. (10)

∴ = .

The shortest distance between the ship and the observation station is 100 km. (12 minutes)

(Method 2) From (1) to △, from sine theorem,

. (8 points)

When the ship arrives, it is the smallest, so it is the smallest.

At this point. (10)

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