Find the time in the following question:

Question

A rocket is fired vertically from the ground. It moves upwards with a constant acceleration of 10ms^-2 for 30 seconds after which the fuel is consumed. After what time from the instant of firing the rocket will attain the maximum height? (g=10 m/s^=-2)

Answer 1

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