# Projectile motion: Finding flight distance with air resistance

proctortom

## Homework Statement

A ball of mass 9N is shot from a slingshot at an angle of 60° from the ground. The slingshot is sitting 1m above the ground. The elasticity of the slingshot is k = 700N/m. Take gravity = 10m/s^2

Air resistance must be taken into account also. Use the formula D = ( C*P*(U^2)*A )/2
D = Drag
C = 1
P = 1.2
U = 13.94
A = 0.03142

How far (in the x direction) has the ball travelled when it hits the ground??

## Homework Equations

F = ma
E = 0.5mv^2
d = vt
d = vt + 0.5at^2
D = ( C*P*(U^2)*A )/2 (D = Drag)

## The Attempt at a Solution

The following calculations have already been found:

Initial force in Ball = 350N
Initial Energy in Ball = 87.5J

Time of flight without air resistance = 5.5sec
X-distance travelled without air resistance = 17.4m

Drag = 3.66 kg/s

I don't know how to apply the air resistance (drag) formula/calculation to what I have found.

## Answers and Replies

voko
This is quite hard as a problem. A 1D problem with quadratic drag could be solved analytically, but in 2D and higher, as far as I know, it can only be solved numerically.