Determining theoretical range

1. Jun 15, 2012

Parkstrailer

1. The problem statement, all variables and given/known data
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.

2. Relevant 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

3. 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?

EP

2. Jun 15, 2012

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.

Last edited: Jun 15, 2012
3. Jun 15, 2012

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.

4. Jun 15, 2012

Parkstrailer

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

5. Jun 15, 2012

HallsofIvy

Staff Emeritus
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.

6. Jun 16, 2012

LawrenceC

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."