Question

Sandra Bullock and George Clooney are floating together with zero speed in a gravity-free region of space. Sandra has a mass of 90.6 kg, while George has a mass of 118 kg. George pushes Sandra away from him so she can get back to the ship with a final speed of 0.6 m/s. What was George's final recoil speed (in m/s)

Answer 1

`v_g=0.46 (m)/(s)`

Step-by-step explanation:

Because in a gravity free region of space there're not externar folreces on Sandra an George's body, then the total linear momentum in their interaction should be conserved so:

`p_f=p_i`

The final mometum (pf) of Sandra and George should be equal their initial moemntum (pi). Becuase at initial moment they are floatating with zero speed, the initial momentum is zero, the:

`p_f=0`

The final momentum for both is the sum of the momentum of each of them (Pg for George and Ps for Sandra), so:

`p_f = p_s+p_g=0`

`p_s=-p_g`

Linear momentum is defined as mass time velocity, so:

`m_s*v_s=-m_g*v_g`

Solving for the final velocity od George (Vg):

`v_g=-(m_s*v_s)/(m_g)=-(90.6*0.6)/(118)`

`v_g=-0.46 (m)/(s)`

The minus sing indicates the velocity is in the opposite direction to the ship, that means George is going to fly away the ship.