Question

A rocket initially at rest, is fired vertically with an upward acceleration of 10 m/s^2. At an altitude of 0.50km, the engine of the rocket cuts off. what is the maximum altitude it achieves?

Answer 1

Ans is again 0.50 km.
Approach i: common sense indicates that the rocket is travelling first 0.5 km at an acceleration of 10 m/s2 Afterwards it will experience retardation of 10 m/s2 so numerically it will cover the same distance afterwards.
Approach2: Let rocket is fired from A where initial velocity is zero it travels 500 m with a=10 m/s2. applying third equation of uniformly accelerated motion, v2-u2=2as we get v=100 m/s which will act as initial velocity for the remaining journey. Apply the same equation again the answer will be 500m