Projectile motion with varying air resistance

[tyuio2202]

I've seen equations for projectile motion ignoring air resistance and how to solve for the equations of motion when a projectile experiences resistance proportional to its velocity, but how would you determine the equations of motion for a projectile when the air resistance is inversely proportional to the height of the object?

It seems to me like you would start with equations like
may= mg - bvy/ky
max = -bvx/ky

where the projectile has some initial velocity (v0) and angle of elevation ($$\theta$$)

but I don't know how one would go about solving for x(t) and y(t),
or if these equations would even be the way to go.

Any thoughts would be helpful

 

[Vailanor]

. The equations for projectile motion when air resistance is inversely proportional to the height of the object can be determined by using a more general version of the equation for drag force, which is given by F = - bv2/ky, where k is a constant and b is the coefficient of drag. In this case, the coefficient of drag will be inversely proportional to the height of the object, meaning that it will decrease as the height of the object increases. We can then use this information to write the equations of motion for the projectile, which are as follows: mx = m(v0x – bv0x2/ky) my = m(v0y – g – bv0y2/ky) where v0x and v0y are the initial x and y components of velocity, respectively. These equations can then be solved using standard techniques (e.g. integration) to find the position of the projectile at any point in time.