How high and how fast will a 25 kg rocket fly without air resistance?

[David Donald]

Homework Statement

A 25 kg Rocket generates 400 N of thrust. It is designed to burn its fuel for
40 seconds. If launched vertically what will its final vertical velocity be when the fuel runs out? How high can it fly? How long until it reaches the ground? Neglect mass of fuel, and air resistance.

Please check over my work I feel like I may be making a mistake somewhere

Homework Equations

Kinematics Equations

The Attempt at a Solution

First I summed the forces in the Y direction
ΣFy = Ft - Fg = ma
= (400N - 245N)/(25kg) = a = 6.2 m/s^2

Final Vertical Velocity
Vfy = Voy + at
Vfy = 6.2 m/s^2 * 40s = 248 m/s

(Height when fuel runs out)

Yf = Yo + Voy*t + (1/2)a t^2
Yf = (1/2)*(6.2 m/s^2) (40)^2 = 4960 meters

(FINAL HEIGHT)

Vfy = Voy + at
0 = 248 m/s - 9.8m/s^2 t = 25.31 seconds <---- Time of Final Height

Yf = Yo + Voy*t + (1/2)at^2
Yf = 4960m + 248 m/s * 25.31 s = 11385.7 meters

(How Long until it reaches the ground)
I'm confused how to solve this part...

 

[TSny]

Everything looks good up to here:

Yf = Yo + Voy*t + (1/2)at^2
Yf = 4960m + 248 m/s * 25.31 s = 11385.7 meters

What about the (1/2)at² term in the equation above?

(How Long until it reaches the ground)
I'm confused how to solve this part...

Can you specify in more detail what is confusing your here?

 

[David Donald]

I forgot to include the negative acceleration due to gravity right?
i'm not sure how to find the time of max flight...

 

[TSny]

I forgot to include the negative acceleration due to gravity right?

Right.

i'm not sure how to find the time of max flight...

Not sure what you mean by "max flight". Try to find the time from "burn out" until the rocket hits the ground. During this time the rocket is in free fall.

{EDIT: Or, you can try to find the time from the point of max height until the rocket hits the ground. This will be easier. You already know the time to reach max height.}

 

[David Donald]

Nevermind I figured it out, thank you!