A destroyer ship goes after an enemy ship in a straight line, the enemy ship seems
the captain of the destroyer as it moves with speed . a way from him, ther
the destroyer fired a torpedo with a speed . to hit the enemy ship after
3 minutes, then the distance between the destroyer and the ship at the moment of
firing the torpedo .

To solve this, we first need to calculate the distance the enemy ship has traveled in 3 minutes. Since it’s moving at 18 km/hr, we convert 3 minutes into hours, which is 0.05 hours. The distance traveled by the enemy ship is then:

Distance = Speed × Time = 18 km/hr × 0.05 hr = 0.9 km.

Next, we find the distance the torpedo travels in 3 minutes. With a speed of 108 km/hr:

Distance = Speed × Time = 108 km/hr × 0.05 hr = 5.4 km.

When the torpedo is fired, it must cover the distance to the moving enemy ship, which has already traveled 0.9 km away by that time. Thus, the initial distance between the destroyer and the enemy ship when the torpedo is fired is:

Distance = Distance covered by torpedo + Distance covered by the enemy ship = 5.4 km + 0.9 km = 6.3 km.

However, since the problem asks for the distance at the moment of firing the torpedo, we consider the distance the torpedo would have covered in 3 minutes only, implying an initial distance of 5.4 km at the moment of firing. Therefore, the answer is:

(a) 5.4 km.

But, if you were looking for the distance at which you caught up accounting the enemy movement in that timeframe, which is the exciting twist in this scenario, you’d root for a 6.6 km option added as the combination of both. Fun as it sounds, the true answer remains 5.4 km as accurately specified for the torpedo’s trajectory covered during its travel. Enjoy those nautical numbers!