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A battle ship cruises directly towards an island at 50 km/hour?
that has a 3,000 meter high mountain with the peak 2,000 meters from an enemy fort on the side exactly opposite the ship.
The ship's captain orders his gunners to attack the enemy fort with the 16 inch guns the moment the ship reaches the nearest position to fire.
The gunners have the option of firing the guns at 1,000 m/s
or 800 m/s and any angle from 15 degrees to 60 degrees. The shells each weigh 1,000 kg.
If the ship is 150 km from the peak when the order is given when is the optimal time, muzzle velocity and angle of the guns?
Ignore the curvature of the Earth, air resistance and assume the fort is on the same horizontal plane as the ship's guns.
The shot must clear the mountain and strike the fort. The shot will be from the front of the ship. The ship maintains constant speed throughout the maneuver.
the maximum distance is correct. The question is asking when is the time to shoot since the ship is cruising towards the island at 50 km/hr there will be a time that the shell will clear the mountain at the correct trajectory to strike the fort.
2 Answers
- 1 decade agoFavorite Answer
Hmm... according to my calculations, it is physically impossible for the ship to bomb the fort.
Because the fort and the ship are on the same horizontal surface, the bullet will travel the farthest when the muzzle velocity is 1000 m/s and the angle is 45 degrees. (best case scenario)
Voy = 1000sin45 = 707 m/s
Vfy = -Voy = -707 m/s
Vfy = Voy + at
-707 = 707 - 9.8t
t = 144 seconds
Vox = 1000cos45 + 13.9 = 721 m/s
The 13.9 is from the velocity of the ship.
x = Voxt = 721 * 144 = 103824 meters
In the best case scenario, the shells will travel 103824 meters, short of the 152000 meters required to bomb the fort... letting alone going high enough to go over the mountain.
