what is the maximum height reached by the rocket?

Question

A model rocket is launched straight upward with an initial speed of 48.3 m/s. It accelerates with a constant upward acceleration of 2.23 m/s^2 until its engines stop at an altitude of 160 m. The acceleration of gravity is 9.81 m/s^2. Answer in units of m.

Answer 1

Let us find out its speed at the time, engine is shut off.

 

V^2 = U^2+2as

 

a --- acceleration

V -- final velocity

U -- initial velocity

s -- altitude

 

V^2=(48.3)^2+2*2.23*160

 

       =3046.49

 

From this height onwards the rocket goes up under gravity

 

0=(3046.49)^2-2*9.81*s

 

s=155.3 Mt

 

So, total altitude =155.3+160

 

                         =315.3 Mt