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,