Answer
The final velocity of the space probe is $~~108.3~m/s$
Work Step by Step
We can use Equation (9-88) to find the final velocity of the space probe:
$v_f-v_i = v_{rel}~ln(\frac{M_i}{M_f})$
$v_f = v_i + v_{rel}~ln(\frac{M_i}{M_f})$
$v_f = (105~m/s) + (253~m/s)~ln(\frac{6170~kg}{6090~kg})$
$v_f = 108.3~m/s$
The final velocity of the space probe is $~~108.3~m/s$
