How long does it take for a rocket to lift off the ground?

[Tj Nelson]

Homework Statement

A rocket with an initial mass of 60,000kg ignites its engines and burns fuel at a rate of 300 kg/s with an exhaust velocity of 2220 m/s. How long after the engines start does the rocket lift off the ground?

Homework Equations

From Newton's second law
F = Ma this equation can be derived
M(dv/dt) = Fext + u(dm/dt)

The Attempt at a Solution

I think the solution is fairly simple. What I did is divide by m, Fext = mg, and integrated it to get
ΔV = uln(mi/mf) - gΔt. But we don't know what the velocity of the rocket...

 

[TSny]

There is no need to integrate the equation to find change in velocity. You are only interested in when the rocket lifts off the ground.

What is the condition on the amount of thrust in order for the rocket to start moving upward?

 

[Tj Nelson]

The thrust has to be greater than the force of gravity acting on it for the rocket to get off the ground, which is true in this case.

 

[TSny]

Right.

 

[Tj Nelson]

Ok so the forces are opposing each other at liftoff so ΣFy = Ft- mg =ma . But it does not make sense to me how you can get the time it takes to liftoff from that.

 

[TSny]

If the thrust force is greater than the weight of the rocket when the engines are first turned on, then how long do you have to wait before the rocket lifts off?

(This would have been a more interesting problem if the initial weight of the rocket were less than the thrust.)

 

[Tj Nelson]

Okay. If the weight of the rocket were less than the thrust, then I assume we would not be able to lift it off.

 

[TSny]

Okay. If the weight of the rocket were less than the thrust, then I assume we would not be able to lift it off.

Not at first. But if you wait ...