Unbalanced force to find altitude of airplane

[a_r_part]

Homework Statement

An airplane with a mass of 3,000 kg flies horizontally at a constant speed. The airplane then increases its horizontal speed and the lift force produced by its wings increases to 30 kN, increasing the airplane’s altitude. How much has the airplane’s altitude increased by when it has an instantaneous upward velocity of 25 m/s?

Relevant Equations

F=ma

Since the airplane is flying at a constant speed, then the lift force equals the weight of the airplane. This means that the lift force prior to acceleration is the mass * gravity constant = 29400 N.

When the airplane increases horizontal speed, the lift force increases to 30 kN. This means, using Newton's Second Law, that the acceleration is 0.2 m/s/s.

This is where I get lost: the question asks about altitude given speed. The formulas for projectile motion come to mind, but I don't know how to set them up.

Could someone provide hints for me to arrive at the answer?

 

[haruspex]

Homework Statement:: An airplane with a mass of 3,000 kg flies horizontally at a constant speed. The airplane then increases its horizontal speed and the lift force produced by its wings increases to 30 kN, increasing the airplane’s altitude. How much has the airplane’s altitude increased by when it has an instantaneous upward velocity of 25 m/s?
Relevant Equations:: F=ma

I haven't been able to find a solution.

Per forum rules, please post an attempt.
Hint : How much was the lift force before the plane's speed increased?

 

[hmmm27]

Since the airplane is flying at a constant speed, the lift force before acceleration is zero.

That would make it not so much an "airplane" as a "hole in the ground". The question specifically states "flying horizontally".

 

[Lnewqban]

 

[kuruman]

This is where I get lost: the question asks about altitude given speed. The formulas for projectile motion come to mind, but I don't know how to set them up.

Stay away from the projectile motion equations. They apply to objects in free fall. An airplane in free fall is not a good thing, especially for its passengers.