This question is a long freeresponse question. Show your work for each part of the question. V0 \\\\ +x Sphere' '\\ \\ +y >\"\\' Floor _\\ Motion of a Sphere Students are studying the two-dimensional motion of objects as they move through the air. Specically, they are examining the behavior of a sphere that is launched horizontally from a location above the oor with an initial velocity 1:0 in the +9: direction, as shown in the gure. The students assume that the positive directions are along the sphere's initial velocity for horizontal motion and downward for vertical motion. The horizontal displacement of the object from its starting point is 1:, and the vertical displacement of the object from its starting point is y. One of the students derives an equation for y in terms of a: and other quantities. After examining the equation, the student claims that y is proportional to :52. (a) Derive an equation for the vertical coordinate yof the sphere as a function of at. 1:0, and physical constants. as appropriate