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 y(t) = RE3/2 + 3 g 2 REt 2/3 where RE is the radius of the Earth (6.38 ✕ 10^6 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (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.) vy(t) = √ g 2 2R E (R ( 3 2 ) E +3√ g 2 R E t)(− 1 3) m/s ay(t) = m/s2 (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.) This answer has not been graded yet. (c) When will the rocket be at y = 4RE? Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. s (d) What are vy and ay when y = 4RE? (Express your answers in vector form.) vy(t) = m/s ay(t) = m/s2