Question

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 44.1m/s^2 . The acceleration period lasts for time 7.00s until the fuel is exhausted. After that, the rocket is in free fall. Find the maximum height y_max reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 rm{m/s^2} .

Answer 1

The acceleration and distance is related to the following expression:
y=v0*t + a*t^2/2 ; v0=0 
y=44.1*100/2 = 2205m 
hence, the speed will be 
v=0 + a*t = 441m/s 
from that height it will just be subjected to the gravitational acceleration 
0=v_acc^2 -2g*y_free 
y_free = v_acc^2/2g = 9922.5m 
y_max = y_acc+y_free = 441+9922.5 =10363.5m