A particle is projected radially outward from a planet with speed $v_e/√2.$ Its maximum distance from the planet's centre is:
Options

Question

A particle is projected radially outward from a planet with speed v_e/√2. Its maximum distance from the planet's centre is:

G1 Physics · Accepted Answer

Since v_e²=2GM/R, the launch speed satisfies v²=GM/R. Initial E=GMm/(2R)−GMm/R=−GMm/(2R). At turning point E=−GMm/r_max, so r_max=2R.