A projectile is launched vertically from the surface of the Moon with an initial speed of 1410 m/s. At what altitude is the projectile's speed one-half its initial value?
here ,
mass of moon , m = 7.35 *10^22 Kg
radius ,r = 1737 km = 1.737 *10^6 m
Using conservation of energy
0.50 * M * (1410)^2 - 6.673 *10^-11 * 7.35 *10^22 * M/(1.737 *10^6) = 0.50 * M * (1410/2)^2 - 6.673 *10^-11 * 7.35 *10^22 * M/(1.737 *10^6 + h)
0.50 * (1410)^2 - 6.673 *10^-11 * 7.35 *10^22/(1.737 *10^6) = 0.50 * (1410/2)^2 - 6.673 *10^-11 * 7.35 *10^22/(1.737 *10^6 + h)
solving for h
h = 623165 m = 6.23 *10^5 m
the height for the half height is 6.23 *105 m
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