# Air resistance in projectile motion

1. May 31, 2010

### cmorency

Does anyone know how to find a formula for air resistance if i shoot an object at a 0 degree angle and know mass, time, distance travelled, drop and initial velocity?

I got to Air Resistance (AR) For Vertical Drop: AR=1/2 g((∆s_h)/V_ih )^2)-∆s_v

g = gravity
∆s_h= delta distance horizontal
V_ih = horizontal initial velocity
∆s_v= delta distance vertical

This is just for difference in distance. What would a unit that i could use to describe air resistance be?
I may be and probably am completely off so if i am please correct me. Thanks so much if you can help me.

2. May 31, 2010

### rock.freak667

I guess you could use http://en.wikipedia.org/wiki/Drag_equation" [Broken]

In essence drag comes down to this FD∝v for lamina flow and FD∝v2 for turbulent flow.

Last edited by a moderator: May 4, 2017
3. May 31, 2010

### cmorency

what would my drag coefficient be though?

4. May 31, 2010

### rock.freak667

you'd need to look that up as that depends on the geometry of your mass.

5. May 31, 2010

### cmorency

thanks! i think i figured it out.

6. May 31, 2010

### pgardn

The units would be Newtons and it would be a resisitve force.
There is a standard formula to describe resistive forces or drag forces that goes something like this:

Fdrag = Cv^n

The C is a constant that depends on the projectile and the air/fluid. Paper obviously would have a larger C than lead in air. The shape of the projectile also comes into account. Lead spread out in a thin shell would have a diff C than lead in a spherical shape. This is all sort of contrived as the experimental variables really do a lot to shape the equation to help describe a resistive force.

The v is velocity and it is raised to some power n, again to try and mimic the experiment. Bottom line is the faster a projectile moves through the air, the larger the resistive force.

Hope this helps some.

For your particular problem, the resisitive force horizontally would start out very high if you shot a projectile from a gun with a large muzzle velocity, while the reisistive force in the vertical would start out at zero and get bigger as the projectile starts out at rest in the vertical if shot perfectly horizontally (0 degrees).

OK...
While I was typing a lot got done.

7. Jun 1, 2010

### cmorency

What would the mass density mean? Is it of the air and how would i calculate this?

8. Jun 1, 2010

### rock.freak667

the density ρ, is the density of the fluid that the mass is falling through, in this case it is air. Just note that density changes with temperature.