Planet x orbits the star omega with a "year" that is 150 earth days long. planet y circles omega at four times the distance of planet x. how long is a year on planet y?

1200 days

Explanation:

According to the Kepler's Third Law: "The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.”

Using above statement we get,

Tx^2/rx^3 = Ty^2/ry^3

Rearranging the above terms for we get,

days

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