In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by r(t) = (RE3/2 + 3\\/ 2Ret) ; where RE is the radius of the Earth (6.38 x 10 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s-). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.) V , ( t ) = m/s) j ay(t) = m/s2) j (b) Plot y(t), vy(t), and ay(t). (A spreadsheet program would be helpful. Submit a file with a maximum size of 1 MB.) Choose File no file selected This answer has not been graded yet. (c) When will the rocket be at y = 4RE? S (d) What are vy and ay when y = 4RE? (Express your answers in vector form.) V, (t ) = m/s a (t) = m/$2