$(10)$ Problem $20,$ chapter $7.$ A two$-$stage rocket moves in space at a constant velocity of $4700\frac{m}{s}.$ The two stages are then separated by a small explosive charge placed between them. Immediately after the explosion the velocity of the $1000-$kg upper stage is $5500\frac{m}{s}$ in the same direction as before the explosion. What is the velocity $($magnitude and direction$)$ of the $2100-$kg lower stage after the explosion? Before the explosion:

After the explosion: