Sep 23, 2009 at 4:51 PM
Edited Sep 23, 2009 at 4:54 PM
Hi there, more than an engin question, is a physics question. This is what I'm doing:
I have a body with mass M, in an environment with gravity G. I need to know how much impulse I need to make the object "jump" to a certain point in the world.
First for the height (the Y factor) I know that the impulse is the delta of the momentum, and I know that:
D = Vi + 1/2 * A *T^2
(D = Distance traveled, Vi = initial velocity, A = Acceleration, in this case the gravity in negative, T = time)
And the velocity is
Vf = Vi + A*T
(Vf = final velocity)
I want, of course my final velocity to reach 0 when it arrives to destination, so making Vf = 0, I get that Vi = -A*T, and as the gravity is the acceleration (in negative), I have Vi = G*T. Replacing this I have in the first equation:
D = G*T - 1/2 * G * T^2
1/2*G*T^2 - G*T + D = 0
I know D, I know G, I need to know T. Using Baskara formula I have that:
T = (G +- SQRT((-G)^2 - 4 * 1/2*G * D))/2*1/2*G
Now I have the time needed to jump to that height. Returning to the first equation (D = Vi + 1/2 * A *T^2), if I multiply everything by the body's mass I get:
D*M = Vi*M + 1/2 * A * T^2 *M
The impulse is the difference of the momentum (Velocity * Mass), so replacing Vi*M by impulse (I), I get:
D*M = I + 1/2 * A * T^2*M
Then I have the needed impulse I.
But that isn't working for me. What I'm I doing wrong? Please help!