Using the following formulas for projectile motion:
Height, H = ( Vo^2 * sin theta^2 )/g
Range, R = ( Vo^2 * sin 2*theta )/g
Rearranging in terms of Vo^2:
Vo^2 = gH / sin theta^2
Vo^2 = gR / sin 2*theta
Equating the two formulas to each other to solve for the angle theta:
gR / sin 2*theta = gH / sin theta^2
Substituting the given values:
(9.8)(111) / sin 2*theta = (9.8)(72.3) / sin theta^2
angle = 52.36 degrees
Therefore, the angle of launch is approximately 52.36 degrees.
