A projectile fired from the point (0, 0) at an angle to the positive x-axis has a trajectory given by

where

x = horizontal distance in meters

y = height in meters

v = initial muzzle velocity in meters per second (m/sec)

g = acceleration due to gravity = 9.81 meters per second squared (m/sec²)

c > 0 is a constant determined by the angle of elevation.

A howitzer fires an artillery round with a muzzle velocity of 897 m/sec.

(a) If the round must clear a hill 200 meters high at a distance of 2000 meters in front of the howitzer, what c values are permitted in the trajectory equation?

(b) If the goal in part (a) is to hit a target on the ground 75 kilometers away, is it possible to do so? If so, for what values of c? If not, what is the maximum distance the round will travel?

2 _y = cx (1 + c ( )( )