Calculate impulse need on object to throw i Y meters into the air, with varying mass

Question

Say I have an object that has a variable mass. Now I want to apply a vertical impulse (straight up into the air) onto the object, so it always flies up to the same height. How do I calculate this?

So the variables are:

m: mass
Y: height (constant)
If: Impulse force
G: Gravity

The origin is always from a floor, so no mid-air impulses or anything.

(I'm using the Box2D engine, but I think that a solution would be engine independent?)

Answer 1

The potential energy of the object at its apex is m*g*h where g is the acceleration due to gravity, m is the mass of the object, and h is the height you want it to go to. We want the initial kinetic energy, 1/2*m*v^2 to be equal to the final potential energy. So we have

2*m*g*h=m*v^2

Impulse is defined as Force*time, so F*t=m*a*t, but under constant acceleration a*t=v, so we have Impulse=m*v. Solving for v and plugging in we have: 2*g*h=v^2=Impulse^2/m^2

Impulse=Sqrt(2gh)*m.

Answer 2

it really depends on how long do you want to apply the force.

but for starter you can use m*g*Y = f*dy in which f is the force you are applying and dy is how far does the object travel before you stop applying the force (which usually is a small value for impulses)