Question

A projectile is launched vertically from the Earth's surface with an initial speed of 10 km/sec....

A projectile is launched vertically from the Earth's surface with an initial speed of 10 km/sec. Neglecting atmospheric drag, how far above the Earth's surface would it go? (Radius of earth = 6380 km)

Homework Answers

Answer #1

Mechanical energy of earth projectile system remains conserved.
Mechanical energy = sum of kinetic +potentil energies
                             = mv2/2 + ( -GMm/r)
M is mass of earth , r is distance between center of earth from mass m and v is speed of mass.
Speed of mass at maximum distance = 0. Hence
100002/2 - GM/R = 0 - Gm/r (r is distance of mass from cenetr of earth)
108/2 - GMR/R2 = - GMR2/R2r
108/2 - gR = - gR2/r    (GM/R2 = g)
108/2 - 9.8*6.38x107 = - 9.8*6.382x1014/r
r = 6.935x107m
distance from earth surface = r - R = 5.55x106m

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