A rocket is fired vertically from the ground with a resultant vertical acceleration of a (10 ~ms ⁻² ). Fuel is finished in (1 ~min ) and it continues to move up. What is the maximum height reached ?

Step-by-step solution

Resultant vertical acceleration, (a=10 ~ms ⁻² ) Height travelled by the rocket in (1 ~min (60 ~s ) ), ( aligned h & =u t+ 1 2 a t^2 & =0 60+ 1 2 10 (60)^2 & =18000 ~m =18 ~km aligned ) Velocity of rocket after (1 ~min (60 ~s ) ), (v=u+a t=0+10 60=600 ~ms ⁻¹ ) After (1 ~min ), when fuel of rocket is finished, then (u=600 ~ms ⁻¹, a=-g=-9.8 ~m / s ^2 ) Hence, if rocket goes at height (h₂ ), then ( aligned v^2-u^2 & =2 g h₂ 0-(600)^2 & =2(-9.8) h₂ h₂ & = 360000 2 9.8 & =18367.3 ~m =18.4 ~km aligned ) ( ) Maximum height