Calculating Time in Dynamics Problem

1. Jan 12, 2010

Theorγ

1. The problem statement, all variables and given/known data
In a hypothetical situation, a rocket has a mass of 100kg, with an engine that emits 21467N. The rocket will fly up from the height of 0m, to the height of 150m. Calculate the time (seconds) it will take for the rocket to reach the height of 150m, with the given data. Air resistance is negligible for this problem.

2. Relevant equations
How long in seconds, will it take the rocket to go from 0m to 150m?

3. The attempt at a solution
I started by calculating the acceleration of the problem.

Force of gravity on the rocket = -9.8 * 100kg = -980N
Force of the engine = 21467N
Sum of all forces = 21467N - 980N = 20487N

Using the Newton's 2nd Law: Sum of all forces = mass * acceleration
20487N = 100kg * acceleration
Acceleration = 204.87 m/s^2

At this point, I have no leads on how to derive time, and would appreciate some help, thanks!

2. Jan 12, 2010

rock.freak667

Use the kinematic equations

v2=u2+2a(s-s0)

s=s0+ut+1/2at2

(s0=initial height)

v=u+at

which one of these three do you think you should use?

3. Jan 12, 2010

Theorγ

The only problem I find with these equations, is how to find velocity.

4. Jan 12, 2010

rock.freak667

If the rocket goes from 0 to 150, then at 0m, the rocket would be at rest.

5. Jan 12, 2010

Theorγ

Okay, so "u" would represent the initial velocity, which would be 0 m/s. Which means the second equation should be used.

s=s0+ut+(1/2)at^2
150m = 0m + 0 m/s * t + (1/2)at^2
150m = (1/2)at^2
1.464 seconds = t^2
t = 1.2101 seconds

Is this valid?

6. Jan 12, 2010

rock.freak667

Yes it looks correct.