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# Suppose that a projectile is launched upward from the earths surface. Assume that the

ISBN: 9780073401102 336

## Solution for problem 22.6 Chapter 22

Applied Numerical Methods W/MATLAB: for Engineers & Scientists | 3rd Edition

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Applied Numerical Methods W/MATLAB: for Engineers & Scientists | 3rd Edition

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Problem 22.6

Suppose that a projectile is launched upward from the earths surface. Assume that the only force acting on the object is the downward force of gravity. Under these conditions, a force balance can be used to derive dv dt = g(0) R2 (R + x)2 where v = upward velocity (m/s), t = time (s), x = altitude (m) measured upward from the earths surface, g(0) = the gravitational acceleration at the earths surface (= 9.81 m/s2 ), and R = the earths radius (= 6.37 106 m). Recognizing that dx/dt = v, use Eulers method to determine the maximum height that would be obtained if v(t = 0) = 1500 m/s

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Suppose that a projectile is launched upward from the earths surface. Assume that the

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