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### Exercise 1.5: Gravitational force

According to Newton's law of gravitation, the action of the gravitational field of the earth on a particle is given by

where is measured from the earth's surface, is the earth's radius, is the gravitational constant, is the mass of the earth, and . There is not simple analytical solution for this problem. Modify your code to simulate the fall of a particle from an altitude with zero initial velocity, and compute its speed when it hits the ground. Determine the value of for which this impact velocity differs by one percent from its value under a constant acceleration . Take the radius of the earth to be .