Artillerymen on a hillside are trying to hit a target behind a mountain on the other side of a river. Their cannon is at (x, y) = (3, 250) where x is in kilometers and y is in meters. The target is at (x, y) = (2, 50). In order to avoid hitting the mountain on the other side of the river, the projectile from the cannon must go through the point (x, y) = (1, 410). Write the equation for the problem. Hi,The physical principle that makes this possible is that if you neglect reststance then the path of the cannonball is a parabola. Suppose the parabola is Since the points (3,250), (2,50) and (1,410) are on the path of the cannonball these points must satisfy the equation. That is 50 = (2)^{2} a  2 b + c and 410 = (1)^{2} a  b + c If you solve these three equations for a, b and c you will have the equation that descrives the path of the cannonball. Cheers,Penny
