In Example 2.6, we considered a simple model for a rocketlaunched from the surface of the Earth. A better expression for arocket's position measured from the center of the Earth is given byy(t) = RE3/2 + 3 g 2 REt 2/3 where RE is the radius of the Earth(6.38 ✕ 106 m) and g is the constant acceleration of an object infree fall near the Earth's surface (9.81 m/s2). (a) Deriveexpressions for vy(t) and ay(t). (Use the following as necessary:g, RE, and t. Do not substitute numerical values; use variablesonly.) 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 spreadsheetprogram would be helpful. Submit a file with a maximum size of 1MB.) This answer has not been graded yet. (c) When will the rocketbe at y = 4RE? Your response differs significantly from the correctanswer. Rework your solution from the beginning and check each stepcarefully. s (d) What are vy and ay when y = 4RE? (Express youranswers in vector form.) vy(t) = m/s ay(t) = m/s2
