Question

Two manned satellites approach one another at a relative speed of 0.230m/s, intending to dock. The first has a mass of 4.50×103kg, and the second a mass of 7.50×103kg. If the two satellites collide elastically rather than dock, what is their final relative velocity?

Answer 1

`v_(f1)=-0.345m/s` ,
`v_(f2)=0.23m/s`

Step-by-step explanation:

The collision is elastically that's means that both mass restore their same value after the collision and don't have the same speed however the collision both satellites approach at the same velocity but in different direction to try to dock so:

`p_i=p_f`

`m_1*v_1+m_2*v_2=m_1*v_(f1)+m_(2)*v_(f2)`

`k_i=k_f`

`1/2*m_1*v_1^2+1/2*m_2*v_2^2=1/2*m_1*v_(f1)^2+1/2*m_1*v_(f2)^2`

Two equations and two variables to find solve to both finals velocities:

`v_(f1)=(m_1-m_2)/(m_1+m_2)*v_1+(2*m_2)/(m_1+m_2)*v_2`

`v_(f1)=-0.345m/s`

`v_(f2)=(2*m_1)/(m_1+m_2)*v_1+(m_2-m_1)/(m_1+m_2)*v_2`

`v_(f2)=0.23m/s`