A particle is projected vertically upward from Earth's surface with speed equal to half the escape speed. Neglect atmosphere. Its maximum distance from Earth's centre is:
Options

Question

A particle is projected vertically upward from Earth's surface with speed equal to half the escape speed. Neglect atmosphere. Its maximum distance from Earth's centre is:

G1 Physics · Accepted Answer

v=v_e/2, so ½mv²=GMm/(4R). Initial total energy=GMm/(4R)−GMm/R=−3GMm/(4R). At maximum radius, −GMm/r_max equals this energy, giving r_max=4R/3.