Question

The total weight of the rocket at t=1.6*10^7 kg.calculate the upwards force on the rocket at this caused by the burning fuel

Answer 1

The diagram shows velocity time graph.

Given is the velocity vs time graph from t = 0 to t = 100 sec.
To find force acting on the rocket due to fuel at t = 80 sec.

In the velocity time curve, the slope gives the acceleration. Marking the velocities at t = 75 s and t = 85 s, gives 900 m/s and 1100 m/s respectively.

Since the graph is nearly linear around t = 80 s:

   a = [v2 - v1]/ [t2 - t1] = 200/10 = 20 m/s²

Mass of the rocket at t = 80 s, m = 1.6 * 10⁷ kg

Net force on the rocket upwards =  m a = 3.2 * 10⁸ Newtons
At t = 80 s, perhaps the rocket has traveled approximately s = 40 km to 60 km
    s << Earth's radius of  6,400 km

So assuming that g remains almost same.

Force downwards due to gravitational attraction = m g' = m g = 1.6 * 10⁷ * 9.81 N
   =  1.57 * 10 ⁸ N

Thus the force (upward thrust ) given by the fuel burning is:
   = (3.2 + 1.57) 10⁸ N
   = 4.77 * 10⁸ N