# Find the maximum height of a rocket fired vertically

1. Dec 2, 2007

### galuda

1. The problem statement, all variables and given/known data
A rocket is fired vertically, ejecting sufficient mass to move upward at a constant acceleration of 2.86g. After 50.2s, the rocket motors are turned off, and the rocket subsequently moves under the action of gravity alone, with negligible air resistance. Ignoring the variation of g with altitude, find the maximum height the rocket reaches.

2. Relevant equations
s = 1/2 at^2

3. The attempt at a solution
I guess during the burn i would use this formula to get .5(2.86*9.8)(50.2)^2, but i don't know where to go after that

2. Dec 3, 2007

### Bill Foster

After the burn, the rocket will still be moving up but will be accelerating down at a rate of 9.8 meters per second squared.

So you can use this:

$$2a(y-y_0)=v^2-v_0^2$$

Where $$y_0$$ is the height of the rocket when the burn stopped. And $$a=-g$$.

3. Dec 12, 2007

### galuda

oh thank you, that worked perfectly