by the concept of momentum conservation we can say
if net force on a system of mass is ZERO then its momentum will remain conserved
Here a ball is projected upwards so if we take Ball + Earth as a system then total momentum of the system will remain conserved
Initially when ball is on the surface of earth the system has zero momentum and hence we can say after throwing the ball momentum of earth + ball must be zero
now using same equation we can say
[tex]P_{ball} + P_{earth} = 0[/tex]
[tex]m_1v_1 + m_2v_2= 0[/tex]
given that
[tex]m_1 = 5 kg[/tex]
[tex]v_1 = 2 m/s[/tex]
[tex]m_2 = 6 * 10^{24} kg[/tex]
from above equation velocity of earth will be
[tex]v_2 = \frac{m_1 v_1}{m_2}[/tex]
[tex]v_2 = \frac{5*2}{6 * 10^{24}}[/tex]
[tex]v_2 = 1.67 * 10^{-24} m/s[/tex]
so above will be the recoil speed of earth
