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Problem 12-33: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12

Course: Engineering Mechanics Dynamics Book: R.C. Hibbeler Chapter: Chapter 12

Question

Question:
As a body is projected to a high altitude above the Earth's surface, the variation of the acceleration of gravity with respect to altitude y must be taken into account. Neglecting air resistance, the acceleration is given by: a equals negative g-naught times R squared over the quantity R plus y, all squared. Here, g-naught is the constant gravitational acceleration at sea level, R is the radius of the Earth, and the positive direction is measured upward. Given g-naught equals 9.81 meters per second squared and R equals 6356 kilometers, determine the minimum initial velocity — the escape velocity — at which a projectile should be shot vertically from the Earth's surface so that it does not fall back to the Earth. The required condition is that v equals zero as y approaches infinity.

Escape Velocity via Separation of Variables

This lesson derives the escape velocity of a projec

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