A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point (x, y) at time t according to the relationship

where ? = the angle of elevation of the launcher and g = the acceleration due to gravity = 32.2 feet/second². An artilleryman is firing at an enemy bunker located 2450 feet up the side of a hill that is 6175 feet away. He fires a round, and exactly 2.27 seconds later he scores a direct hit.

(a) What angle of elevation did he use?

(b) If the angle of elevation is also given by sec ? = ?₀t/x. where ?₀ is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.

2.x cot 0 = 2y + gr"