A projectile is launched vertically from the surface of the Moon with an initial speed of...
A projectile is launched vertically from the surface of the Moon with an initial speed of 1350 m/s. At what altitude is the projectile's speed one-fifth its initial value?
Homework Answers
given that
initial speed vi = 1350 m/s
final speed vf = vi/5 = 1350/5 = 270 m/s
from the conservation of energy
ki-Ui = kf-uf
1/2mvi^2-GmM/r moon = 1/2mvf^2-GmM/r moon to projectile
radius of the moon is = 1737000m
mass of moon M = 7.35*10^22 kg
1/2vi^2 -GM/rmoon = 1/2vf^2-GM/r moon to projectile
1/2*(1350)^2-(6.67*10^-11*7.35*10^22)/1737000 = 1/2(270)^2-(6.67*10^-11*7.35*10^22) /r
911250-2822366 = 36450-4.9*10^12/r
4.9*10^12/r = 1947566
r = 4.9*10^12/1947566
r = 2515960.9 m
altitude h = 2515960.9-1737000 = 778960.9 m
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