Tricky projectile motion question

[johnyk87]

Homework Statement

An enemy ship is on the east side of a mountain island. The enemy ship has maneuvered to within 2500 m of a 1800 m high mountain peak and can shoot projectiles with an initial speed of 250 m/s. If the western shoreline is horizontally 300 m from the peak, what are the distances from the western shore at which a ship can be safe from the bombardment of the ship?

Homework Equations

y= 250m/s*sin(x)t + .5gt^2
x= 250m/s*cos(x)t

R= v^2sin(2x)/g

The Attempt at a Solution

I can set up the problem as a constraint problem. I tried to minimize the range formula subject to the constraint that the projectile will just go over the mountain peak as it passes. The reasoning for this is that I will be able to reduce the range of a shot by shooting it at a slightly higher angle that will just clear the peak. It is not a technical reason but it seems reasonable. I can set up the problem but isolating the angle in my constraint is tricky. Does anyone know of a better way to go about this problem?

 

[kuruman]

As it follows its trajectory, the projectile can clear the mountain top on its way up ( projection angle less than 45^o) or on its way down (projection angle greater than 45^o). So you need to find the angles for which the projectile will just barely clear the top and then find the corresponding ranges. Then look for "blind spots" on the other side.

 

[johnyk87]

Thanks kuruman. I just figured it out a little while ago. I want the angle as it is coming down. For some reason i thought that there would be more than one downward angle that corresponded to just clearing the peak. Thanks again