**Task:**

Consider 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:

where R_{E} 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/s^{2}).

(a) Determine expressions for velocity and acceleration of the rocket

(b) When will the rocket be at ?

(c) What are the velocity and the acceleration when ?

**Solution:**

(a) Velocity of the rocket is

Acceleration of the rocket is

(b) When

(c) The velocity of the rocket when or is

The acceleration of the rocket when or is

**Answers:**

(a)

(b)

(c)

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