(a)Show that if a projectile is launched straight upward from the surface of the earth wit...

(a)Show that if a projectile is launched straight upward from the surface of the earth with initial velocity v0 less than escape velocity then the maximum distance from the center of the earth attained by the projectile

where M and R are the mass and radiusof the earth, respectively. (b) With what initial velocity u0 must such a projectile be launched to yield a maximum altitude of 100 kilometers above the surface of the earth? (c) Find the maximum distance from the center of the earth, expressed in terms of earth radii, attained by a projectile launched from the surface of the earth with 90% of escape velocity.