How Does Air Resistance Affect Theoretical vs Actual Projectile Range?

[Parkstrailer]

Homework Statement

I need to determine theoretical vs actual range of a projectile; but first I must determine initial velocity. The projectile was launched from 1 meter high, at 0° with respect to the horizontal, so I shot it horizontally. The ball landed at a distance of 2.97 meters. My professor wants us to understand how air resistance comes into play, hence determining theoretical vs actual distance.

I've seen many other questions similar to mine, and have tried substituting my numbers in for theirs, but I always seem to be missing one step.

Homework Equations

So far the equation I think works the best to determine initial velocity is ×/ sqrt(2h/g) = Vi
x = distance (2.97m)
h = height (1m)
g = gravity (9.8m/s^2)
Vi = initial velocity

Another equation I found but can't seem to get to work is Vf^2 = Vi^2 +2ad

The Attempt at a Solution

Right now the best answer I think I'm getting is 6.57 m/s for initial velocity, but I am not sure if this is right.

If it is right, how can I use it to determine theoretical range?

Thank you in Advance

EP

 

[LawrenceC]

"Another equation I found but can't seem to get to work is Vf^2 = Vi^2 +2ad"

Above applies to an object accelerating (constant acceleration) with an initial velocity. Your ball does not accelerate in the horizontal direction.

 

[LawrenceC]

How heavy is the ball and what is its size? If it has a high density, then you essentially have calculated the initial velocity because over that distance/velocity, air drag would be almost negligible. If the ball has a low density, then the range and time of flight are both affected to a greater extent.

 

[Parkstrailer]

Can someone atleast tell me if my speed at 6.57 is correct ?

 

[HallsofIvy]

The vertical acceleration is -9.8 m/s^2 so the distance the projectile falls in t seconds is (1/2)(9.8)t^2= 4.9t^2. That tells you that the projectile will descend 1 m and hit the ground when 4.9t^2= 1 or t= sqrt(1/4.9)= .452 seconds, approximately. If it went 2.97 m horizontally in that time, its horizontal speed (neglecting friction) must be 2.97/.452= 6.57 m/s so, yes, that is correct.

 

[LawrenceC]

Can someone atleast tell me if my speed at 6.57 is correct ?

From my previous post: "If it has a high density, then you essentially have calculated the initial velocity because over that distance/velocity, air drag would be almost negligible."