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 }_{0 }[{ R }^{ 2 }/{ (R + y) }^{ 2 }] , where{ g }_{ 0 }is the constant gravitational acceleration at sea level, R is the radius of the earth, and the positive direction is measured upward. If { g }_{ 0 }= 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\rightarrow \infty.