Perform the integral numerically

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The discussion focuses on calculating the time of fall for an object released from a height of 500 km above Earth's surface using numerical integration. The speed of the object at a distance r from the Earth's center is defined by the equation v = sqrt(2GME (1/r - 1/(RE + h)). The integral to determine the time of fall, represented as (Delta) t = - (integral from i to f) dr/v, requires numerical methods for evaluation. Participants emphasize the necessity of adhering to posting guidelines by providing an initial attempt at the solution.

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need help please urgent

An object is released from rest at an altitude h above the surface of the Earth. (a) Show that its speed at a distance r from the Earth’s center, where RE < r < RE + h, is given by
v = sqrt(2GME (1/r -1/ (RE + h) )

(b) Assume the release altitude is 500 km. perform the integral:
(Delta) t = (integral from i to f) dt = - (integral from i to f) dr/v

to find the time of fall as the object moves from the release point to the Earth’s surface. The negative sign appears because the object is moving opposite to the radial direction, so its speed is v = -dr / dt. Perform the integral numerically.
 
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