Why does it take 2 days longer for the Moon to go from New Moon to New Moon when viewed form the Earth than it takes for the the moon to make 1 complete rotation on its axis?

The time between two new Moon phases or two full Moon phases is 29.5 days. ... The difference of 29.5 and 27.3 is that while the Moon is orbiting the Earth, the Earth is moving along in its orbit so it takes longer for the Moon to reach the same position relative to the Sun.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft