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 2/3,. Rt) = (RE/2 + 3,/%REt) j where RE is the radius of the Earth (6.38 x 106 m) and g is the constant acceleration ofan object in free fall near the Earth's surface (9.81 m/sz). a 4 (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: 9, RE, and it Do not substitute numerical values; use variables only.) 3y\") = ( MS); 3m = ( W)!\" (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 le chosen This answer has not been graded yet. (c) When will the rocket be at y = 4RE? S s (d) What are ;y and 3} when y = 4R5? (Express your answers in vector form.) 17y\") = m/5 EN) = m/s2