Consider an airless,non-rotating planet of mass Mand radius R. An electromagneti
ID: 1740492 • Letter: C
Question
Consider an airless,non-rotating planet of mass Mand radius R. An electromagnetic launcherstanding on the surface of this planet shoots a projectile withinitial velocity v0 directed straightup. Unfortunately, due to some error, v0 is less than theplanet’s escapevelocity ve. Specifically,v0 =0.346ve. Unable toescape the planet’s gravitational pull, the projectile risesto a maximal height h above the ground, then falls back to the ground. Calculate the ratio h/Rof the projectile’s maximal height to theplanet’s radius.
Explanation / Answer
Consider an airless,non-rotating planet of mass Mand radius R. An electromagnetic launcherstanding on the surface of this planet shoots a projectile withinitial velocity v0directed straight up. Unfortunately, due to someerror, v0is less than the planet’s escapevelocity ve. Specifically, v0 =0.346ve. Unable toescape the planet’s gravitational pull, the projectile risesto a maximal height h above the ground, then falls back to the ground. Calculate the ratio h/Rof the projectile’s maximal height to theplanet’s radius.
escape velocity on theplanet=2gR
maximum height =u*u/2g
u=0.346Ve =kVe
maximum height=h=k*kVe*Ve/2g=k*k*2gR/2g=k*k*R
now h/R=k*k=0.346*0.346=0.1197