Projectile Motion Problem of a ship

[kdf8]

Okay, I'm in a rut. We got a pack of physics problems from our teacher and no one knows how to go about doing them and he refuses to help us. This is the first one I've ran into major trouble with.

Here's the problem:

An enemy ship is on the east side of a mountainous island, as shown in the figure below. The enemy ship can maneuver to within 2500 m of the 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 enemy ship?

Sorry for such a rough hand sketch, I don't have a scanner.

I've tried working out this problem from doing my own research on projectile motion and basically I know I need to find the smallest and largest angles that will clear the mountain peak and find where those angles will cause the projectile to land, but I have no idea how to do that, equation wise. ANY help will be greatly appreciated.

 

[OlderDan]

Write the equations for x(t) and y(t) for the projectile in terms of the firing angle. Eliminate time from the equations to find y(x). This will be the equation of the path of the shell. It will still depend on the firing angle. What conditions must this equation satisfy for the shell to clear the mountain peak? Satisfying these conditions will determine the limiting values for the firing angle. Once you have those, calculate the range of the projectile.

 

[kdf8]

So would x(t) = 1800(t) + 250*1/2*g*t^2? And then solve out for t and use your t in y(t) = 250sin(theta)t - 1/2*g*t^2 and solve out for theta?

 

[OlderDan]

So would x(t) = 1800(t) + 250*1/2*g*t^2? And then solve out for t and use your t in y(t) = 250sin(theta)t - 1/2*g*t^2 and solve out for theta?

x(t) has an initial velocity term that depends on the angle, and no acceleration. Solve the simpler x(t) equation for time in terms of x and use that expression for time in y(t) to get the equation for y(x).