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21_Dynamics 11ed Manual - Engineering Mechanics Dynamics(b...

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Engineering Mechanics - Dynamics Chapter 12 (b) Terminal velocity means a = 0 0 g 1 cv term 2 () = v term 1 c = v term 100 m s = Problem 12-34 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, this acceleration is determined from the formula a = g [ R 2 / ( R+y ) 2 ], where g is the constant gravitational acceleration at sea level, R is the radius of the earth, and the positive direction is measured upward. If g = 9.81 m/s 2 and R = 6356 km, determine the minimum initial velocity (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. Hint: This requires that v = 0 as y → ∞. Solution: g
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