Question

A 3000 Kg meteorite has a speed of $300m{s}^{-1}$ just before colliding head on with the energy that is the recoil speed of the earth? Mass of the earth = $6\times {10}^{24}Kg$

Answer 1

After hitting earth meteorite stick to the earth surface

Initial velocity of meteorite, $u_1=300m{s}^{-1}$

Mass of meteorite, $m=3000kg$

Initial momentum of earth is zero

Recoil speed of earth = $V$

From conservation of momentum

Final momentum = Initial momentum

$(M+m)V=M_e{u}_2+m{u}_1$

$(6\times {10}^{24}+3000)V=0+3000\times 300$

$V=1.5\times {10}^{-19}m{s}^{-1}$

Hence, recoil to the earth is $1.5\times {10}^{-19}m{s}^{-1}$