Question

Two meteoroids are 2.0×10^{5} km from Earth's center and
heading straight toward Earth. One is moving at 12 km/s , the other
at 20 km/s . a. At what speed will the first meteoride strike the
Earth? b. At what speed will the second meteoride strike the
Earth?

Answer #1

The body-1 (1) and body-2 (2) initial (i) and final (f) velocities v1i, v2i, v1f, v2f;

specific kinetic energies (energy/mass) of the bodies SKE1i, SKE2i, SKE1f, SKE2f;

and also the change in specific potential energy ΔSPE which is the same for both bodies.

G = 6.67428 X 10-11 N-m^2/kg^2, M(earth) = 5.9742X10^{24}
kg.

SPE = -GM/r

Change in SPE from 2.0×105km to r(earth) 6378 km:

ΔSPE = -GM(1/6378000-1/2.0×10^{5)}= 1931156958

The long version:

SKE1i = v1i^2/2

SKE2i = v2i^2/2

SKE1f = SKE1i-ΔSPE

SKE2f = SKE2i-ΔSPE

v1f = sqrt(2SKE1f)

v2f = sqrt(2SKE2f)

Now,

v1f = sqrt(v1i^2-2ΔSPE)

v2f = sqrt(v2i^2-2ΔSPE)

v1 =sqrt(12^{2}-2X1931156958)) = 12831.88217m/s

v2 = sqrt(20^{2}-2X1931156958) = 14258.5887m/s

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