Projectile motion: Finding flight distance with air resistance

AI Thread Summary
The discussion focuses on calculating the flight distance of a ball shot from a slingshot, considering air resistance. The initial parameters include a mass of 0.9 kg, an angle of 60°, and a height of 1 m. Calculations show an initial force of 350 N, an energy of 87.5 J, and a time of flight of 5.5 seconds, resulting in a distance of 17.4 m without air resistance. The challenge lies in applying the drag formula to adjust this distance, as the presence of air resistance will reduce the actual distance traveled. Participants seek guidance on incorporating drag into their calculations to determine the final distance accurately.
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Homework Statement


A ball of mass 0.9kg 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 traveled 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 traveled 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.
 
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I know the distance traveled with air resistance is lower than 17.4m but I don't know how to calculate it.
 

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