# A rocket is launched, it stops accelerating after a period of t but it keeps going up

1. Sep 28, 2011

### Dinovek

1. The problem statement, all variables and given/known data
A rocket is launched off and accelerates vertically up at 10 m/s 2. At 20 seconds, the motors are turned off, but the rocket keeps going up.

a) What height did it reach?
b) What was the time it needed to reach that height?

g: - 9.8 m/s2
a: 10 m/s2
final velocity: 0 m/s (Not sure).
t=20 s

2. Relevant equations
h= vo (t) + g(t)2/2
t=(vf-vo)/g
vo= vf-g(t)

3. The attempt at a solution
I needed to find initial velocity to find height so I did.

vo=vf-g(t)
vo= 0 m/s - (-9.8m/s2)(20)
vo= 196 m/s

Now I just substituted to find height.

h= vo(t) + (g (t)2)/2
h= 196 m/s (20s) + (-9.8 m/s2 (20) 2)/2
h=3920 m + -3920 m/
h= 3920 m - 1960 m
h= 1960 m

I really have no clue how do to even start the problem because I'm not sure what is the time total. I was thinking that after it stops accelerating, every second it decreases 1 m/s on it's acceleration so that would 10 more seconds to the total timing.

Any help would be appreciated it. Thanks.

2. Sep 28, 2011

### VACA

Re: A rocket is launched, it stops accelerating after a period of t but it keeps goin

Why did you use g for acceleration during the first 20 seconds? The rocket is accelerating at +10m/s2 during the first 10 seconds.

You would use g for acceleration after the 20 seconds, since that's when the motors are off.

3. Sep 28, 2011

### Dinovek

Re: A rocket is launched, it stops accelerating after a period of t but it keeps goin

You're right, I didn't read carefully, thanks! I'm not sure how I'm going to calculate the total height. How do I know when it's going to reach final velocity of zero?

4. Sep 28, 2011

### VACA

Re: A rocket is launched, it stops accelerating after a period of t but it keeps goin

You first have to find the height it reaches in the first 20 seconds. Vf will not be zero after 20 seconds. After 20 seconds it is coasting (like a car when you take your foot off of the gas). It will take more time for it to reach 0 m/s (maximum height).

Try solving the coasting part on your own, and post back if you get stumped. Hint:
Vf when the motors are going will be Vo when the rocket is coasting.