How Long Until the Rocket Returns to the Ground?

[lazyboi605]

Homework Statement

A model rocket takes off from ground level accelerating upward at 4.0 g. This upward acceleration lasts for 33 s. Afterward the rocket continues upward, eventually stops rising, then falls back to the ground.

How much time passes from the initial upward acceleration stoping to the rocket returning to the ground?

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

What are your thoughts on how to solve it?

 

[lazyboi605]

I am using velocity/gravity, but it don't seem to work out.

 

[LowlyPion]

I am using velocity/gravity, but it don't seem to work out.

That only gives you the time to max height.

If you want, you can figure that height and then get the time to fall in gravity from x = 1/2*g*t²

Then just add the 2 times together.

 

[lazyboi605]

Would i need to minus 33, because i am trying to find the time passed from initial upward acceleration stopping.

 

[lazyboi605]

Also i don't understand how to find the time to max height. because it will still move after it accelerate.

 

[LowlyPion]

Would i need to minus 33, because i am trying to find the time passed from initial upward acceleration stopping.

V = a*t
So when the engine shuts off, you are going at (4*g)*33 m/s
and dividing by g yields the additional time to max height = 4*33 s.

Now solve for X of engine shutoff X = 1/2 *4*g *t²
That's the point when the engine stops.

Figure the additional height from that point by
V² = 2*g*x

Add the 2 heights - up to engine shutoff and from shutoff to 0 velocity at the top.

Using that height now as your X you have only to solve for the time using

X = 1/2*g*t²

That time to fall + time to max height from engine shut off is what they want.