Calculating Time in Dynamics Problem

[Theorγ]

Homework Statement

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.

Homework Equations

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

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!

 

[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?

 

[Theorγ]

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?

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

 

[rock.freak667]

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

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

 

[Theorγ]

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

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?

 

[rock.freak667]

Yes it looks correct.