A particle is projected vertically from Earth's surface with speed equal to half the escape speed. If its maximum distance from Earth's centre is NR/3, find N.

Question

G1 Physics · Accepted Answer

Initial E=½m(v_e/2)²−GMm/R=GMm/(4R)−GMm/R=−3GMm/(4R). At maximum radius −GMm/r=E, giving r=4R/3. Hence N=4.