A rocket having engines that can provide a thrust of
T = 150 kN is fired from rest. The rocket of mass 4 Mg is initial at rest. Neglecting the loss of fuels and all the other sources of power loss, determine the power output of the engines after 24 s.

1) 99.67 MW
2) 82.25 MW
3) 95.25 MW
4) 96.15 MW

Equation of motion: The accleration with which the rocket travels with a thrust force T is required to be determined first:
S F_y = ma_y
150(10³) - 4(10³)(9.81) = 4(10³) a_c
4000a_c = 110760
a_c = 27.69 m/s²

Velocity of travel v :
v = v_o + a_ct
v = 0 + 27.69t = 27.69t
velocity (v) = 27.69(24) = 664.56 m/s

Power : The power output can be obtained as
P = T. v = 150(10³) (664.56) = 99.67(10⁶) W
P = 99.67 MW

So the power output of the engines as a function of time is P = 99.67 MW