Thank you for answering part of the question...Need help with the rest.
Have figured out that 36 degrees is the minimal angle that the ship can fire to make it over the hill and 76 degrees is the maximum. The ship is safe if it is; closer than 194 meters to the western side and further than 3577 meters. However, the answer in the back of book is; less than 265 and greater than 3280 meters. What am I doing wrong?
An enemy ship is on the east side of a mountainous island. The enemy ship can maneuver to within 2500 meters of the 1800 meter high mountain peak and can shoot projectiles with an initial speed of 250m/sec. If western shoreline is horizontally 300 meters from the peak, what are the distances from the western shore at which a ship can be safe from the bombardment of the enemy ship?
you have to be farther than 2500 meters from the shoreline because of the enemies trajectory. your angle of fire should then be higher than at least 60
Use 45 degrees for the max range of the ships shooting.
To determine the distances from the western shore at which a ship can be safe from the bombardment of the enemy ship, we need to analyze the projectile motion of the enemy ship's projectiles.
1. Calculate the time it takes for the enemy ship's projectiles to travel to the peak of the mountain:
- The height of the mountain is 1800 meters.
- The initial vertical velocity of the projectiles is 0 m/s since they are fired horizontally.
- The acceleration due to gravity is 9.8 m/s².
- Use the equation h = ut + (1/2)gt², where h is the height, u is the initial vertical velocity, g is the acceleration due to gravity, and t is time.
- Rearrange the equation to solve for t: t = sqrt(2h/g).
- Calculate t: t = sqrt(2 * 1800 / 9.8).
2. Calculate the maximum horizontal distance the projectiles can travel:
- The initial horizontal velocity of the projectiles is 250 m/s.
- The time of flight for the projectiles is 2t since they have symmetrical motion.
- Use the equation d = ut, where d is the distance and u is the initial horizontal velocity.
- Calculate the maximum distance: d = 250 * 2t.
3. Determine the minimum and maximum angles the ship can fire with:
- The ship must fire above an angle of 60 degrees to be farther than 2500 meters from the shoreline.
- The maximum angle for the ship's shooting is 45 degrees.
4. Calculate the minimum and maximum distances from the western shore at which the ship is safe:
- The ship is safe if it is closer than 2500 meters to the eastern side of the mountain but further than 300 meters from the peak on the western side.
- Subtract the maximum distance of the projectiles from the minimum distance allowable from the shore: 2500 - (300 + d).
The answer in the back of the book may have been obtained by calculating the exact distances using the given parameters, or there may be some other factor to consider that is not mentioned in the problem statement. Double-check your calculations to ensure there are no errors.