What Is the Recoil Speed of Earth After a Meteorite Collision?

[Idividebyzero]

1.Use 5.98 × 1024 kg as the mass of the Earth.
A 1680 kg meteorite has a speed of 184 m/s
just before colliding head-on with the Earth.
Determine the recoil speed of the Earth.
Answer in units of m/s.



2. (m1+m2)vf=m1v1i+m2v2i



3. used the equation for a perfectly inelastic collision in which the meteor strikes and embeds itself in the Earth causing the Earth to recoil. the Earth being more massive this recoil velocity would be insignificanly small relative to persons on Earth anyways, solved for vf by m1v1i+m2v2i/(m1+m2) taking the Earth to be at rest initially. getting 5.2e-20 which is incorrect. i suppose I am supposed to take kinetic energy into the equations but i don't see how

 

[Idividebyzero]

also tried

V'b= Va(2Ma/Ma+Mb) + Vb(Mb-Ma/Ma+Mb)
V'b=184(2*1680)/(1680 + 5.98e24) + 0
getting V'b=1.03e-19

i don't know maybe i need to take the Earth's rotation into account

nevermind this fails as its for elastic collisions only

 

[Idividebyzero]

also figured being a recoil the sign would be opposite, solved using elastic collision i get the same answer. 1.03e-19 but positive and negative incorrect

 

[Idividebyzero]

bump i need help

 

[ehild]

The question is that the speed of the satellite is given with respect to the Earth or with respect to the Sun. If it is with respect to the Earth then your method in the first post is correct, but give the result with one more significant digits.

ehild

 

[Idividebyzero]

i added more sig figs like you suggested and it was correct. 5.17e-20