Answer
(a) $F_T = 3.96~N$
(b) $F_T = 2.32~N$
Work Step by Step
Let $F_T$ be the rocket's thrust.
(a) $\sum F = ma$
$F_T - mg = ma$
$F_T = m(g+a)$
$F_T = (0.200~kg)(9.80~m/s^2+10~m/s^2)$
$F_T = 3.96~N$
(b) $\sum F = ma$
$F_T - mg_M = ma$
$F_T = m(g_M+a)$
$F_T = (0.200~kg)(1.62~m/s^2+10~m/s^2)$
$F_T = 2.32~N$