The arrows show the direction of rotation of the merry-go-round, which moves with a constant speed, moves with a constant speed causing a shift of 45? . assuming a child sitting in the center attempts to throw the ball directly to child d, which child will likely catch the ball?

This question is lacking especially the diagram, well I've read the entire question and seen its diagram and it demonstrates a Coriolis effect. The child that could get the ball would be child c. Well Coriolis effect is the deflection of a free moving object, such as ball, due to a rotation of the merry go round.

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.