Engineering Mechanics - DynamicsChapter 12(b)Terminal velocity means a= 00g1cvterm2−()=vterm1c=vterm100ms=Problem 12-34As a body is projected to a high altitude above the earth’s surface, the variation of the accelerationof gravity with respect to altitude ymust be taken into account. Neglecting air resistance, thisacceleration is determined from the formula a= g−[R2/(R+y)2], where gis the constantgravitational acceleration at sea level, Ris the radius of the earth, and the positive direction ismeasured upward. If g= 9.81 m/s2and 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 itdoes not fall back to the earth. Hint:This requires that v= 0 as y→ ∞.Solution:g
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