- #1

johnyk87

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## 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?