Solution:
The distance travelled by the rocket during consumption of fuel ( 30 sec.) in which resultant acceleration is vertically upwards i.e 10 m/s2 will be
h = ut + 1/2gt2
h = 0*30 + 1/2*10*302 = 4500m --------------------(1)
Velocity will be
v = u +at
v = 0 + 10*30 = 300m/s ---------------(2)
As after the fuel is consumed the initial velocity from eqn. (2) is 300 m/s and gravity opposes the motion of rocket, so from 1 st equation of motion time taken by it to reach the maximum height (for which v = 0)
v = u – gt
0 = 300 – 10t
t = 30 sec