Question

if a 5-kg bowling ball is projected upward witha velocity of 2.0 m/s, then what is the recoil velocity of the Earth(mass=6.0×10^24kg)

Answer 1

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

$P_{ball} + P_{earth} = 0$

$m_1v_1 + m_2v_2= 0$

given that

$m_1 = 5 kg$

$v_1 = 2 m/s$

$m_2 = 6 * 10^{24} kg$

from above equation velocity of earth will be

$v_2 = \frac{m_1 v_1}{m_2}$

$v_2 = \frac{5*2}{6 * 10^{24}}$

$v_2 = 1.67 * 10^{-24} m/s$

so above will be the recoil speed of earth