- #1
swbluto
- 12
- 0
[Differential equation at the end; All the intermediary stuff is the problem behind it.]
I was curious about finding the velocity function for a free-falling object using solely Newton's equations. Using the force diagram, I've deduced that
m-mass
g-gravitational constant
f_net - net force
A - cross-sectional area
v - velocity
f_net = mg-1/4Av^2
ma = mg - (Av^2)/4
a=g-(Av^2)/4m
v'=g-(Av^2)/4m and g, A and m are constants. In this case, I simplified by assuming A=1, m=1 so the equation becomes the nonlinear first-order differential equation
v'=9.8-.25v^2. How do you... solve this kind of equation?
I was curious about finding the velocity function for a free-falling object using solely Newton's equations. Using the force diagram, I've deduced that
m-mass
g-gravitational constant
f_net - net force
A - cross-sectional area
v - velocity
f_net = mg-1/4Av^2
ma = mg - (Av^2)/4
a=g-(Av^2)/4m
v'=g-(Av^2)/4m and g, A and m are constants. In this case, I simplified by assuming A=1, m=1 so the equation becomes the nonlinear first-order differential equation
v'=9.8-.25v^2. How do you... solve this kind of equation?