Answer
The total kinetic energy after separation is $~~1.275\times 10^{10}~J$
Work Step by Step
In part (a), we found that after separation, the speed of the rocket case is $~~7290~m/s$
In part (b), we found that after separation, the speed of the payload is $~~8200~m/s$
We can find the total kinetic energy after separation:
$K = \frac{1}{2}(290.0~kg)(7290~m/s)^2+\frac{1}{2}(150.0~kg)(8200~m/s)^2$
$K = (7.706\times 10^9~J)+(5.043\times 10^9~J)$
$K = 1.275\times 10^{10}~J$
The total kinetic energy after separation is $~~1.275\times 10^{10}~J$
