Suppose that a projectile is launched straight upward from the surface of the ea

Question

Suppose that a projectile is launched straight upward from the surface of the earth on the equator with initial velocity v0. Find the position function r(t) if there is no air resistance Fr=0 and gravitation is Fg=-gama(Mm/r^2), where Me=5.975*10^24 kg denoting mass of the earth, gama=6.6726*10^-11 m/kg^2 denoting the gravitation constant, m is the mass of the projectile, r is the distance from the center of the earth,r>or=R=6.378* 10^6 m the equatorial radius of the earth.  Find the maximum distance rmax from the center of the earth attained by projectile.  Find the minimum escape velocity v0 when rmax=infinity.

Explanation / Answer

(1) for given maximum altitude = h = r(max)-R_E r(max)= h+R_E v_i^2 = 2GM_E(1/R_E-1/rmax) 1/rmax = v_i^2/2GM_E-1/RE = (v_0^2/2*6.6726*10^-11*5.975*10^24)-1/6.378*10^6 (2) escape speed = sqrt(2GM_E/R_E) = sqrt(2*(6.67*10^-11N.m^2/kg^2)(5.98*10^24)/6.37*10^6) = 1.12*10^4 m/s

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