# Initial speed of a football when average speed is known

by fsk08
Tags: average, football, initial, speed
 P: 3 Hi First of all, this is not a homework question, but I'm sorry if it's in the wrong sub-forum. I know that a football (soccer) has been kicked a distance of 5 meters using 0,16 seconds, that would give an average speed of 112,5 km/h, or approx 31 m/s. But since the speed of a football is given as inital speed, Vo, and not average speed, I was wondering if there is a way to figure out the initial speed when the average speed is known. Since the ball has no contact with the ground during the 5 meter flight, I guess that the only factor that reduces speed is drag/air resistance. I have tried to use the drag equation, but ended up with some extreme numbers which had to be wrong. I can provide some exact entry values regarding the football itself (weight, circumference etc) if its needed. I did find out that a baseball loses 1 mph per 7 feet of travel as a rule of thumb, which translates into roughly 1,5 kmh for every 2 meters. But I would guess that a football would lose more speed per meter than a baseball, because of the difference in size and weight. I guess the most simple way to find out the initial speed is to compare the aerodynamics of a baseball vs a football, and then use this rule of thumb to calculate the approx initial speed. But I don't know how more aerodynamic a baseball is compared to a football... Any thoughts on this?
 P: 948 My initial thoughts are: 1) If it's a homework question, let's move it to the homework section. 2) Rules of thumb are probably not a good idea if you want an accurate answer. 3) Essentially you are asked to make some conclusion about what the graph of speed vs. time is. From the 'general' equation you would be able to plug in some numbers and solve completely. 4) Can you show your math for the drag equation?
 P: 3 Not homework, just a "want to know"-question. Regarding the drag equation, I did not know what to do after I found the force on the ball due to drag. The formula is: F = 0,5( P x U2 x Cd x A) P=mass density of air=1,225 kg/m3 U=velocity of the football=31 m/s (Average speed) Cd=drag coefficient=0,25 (according to a NASA document I found) A=reference area (the area of the football which the air "hits" during flight?)=0.03792 mē F=5,58 N Then what? This is where I am stuck. And I'm not even sure if my math and use of the equation is correct..
P: 3

## Initial speed of a football when average speed is known

I got a suggestion from a friend in how to solve this, but I'm not sure if its 100% correct.

The force from the drag was calculated in my previous post to be 5,58 newton. Since the ball traveled 5 meters, then its:

5,58 N x 5 m = 27,9 joule

E-kinetic = 0,5(m x v2)

So, if I know the final velocity of the ball (after 5m), then I should be able to calculate the initial speed right? Or am I wrong? In my head its like this:

Initial kin energy = Final kin energy + energy from drag

E-ini = E-fin + 27,9 J

But then I have to assume the final velocity of the ball, since all I got is the average speed. So then the final answer will be unaccurate. But lets assume, just for the example, that final vel was 108 kmh, or 30 m/s. The football weights 0,442 kg.

E-ini = 0,5(0,442 kg x 30 ms x 30 ms) + 27.9 J
E-ini = 226,8 J
Multiplies by 2, divides by mass (0.442 kg), and then square root to find initial velocity

Vo = 32 m/s = 115 kmh

Is this correct? Again, I'm pretty weak at physics, and this was with help from a friend (who insists he ain't that good at physics either). But the problem with this "solution" is that I had to guess the final velocity..
 P: 267 In 5 meters, a football will not lose that much speed, assuming the only retarding force is drag. Consider a footballer shooting from the penalty spot. That is 11 meters away, over twice your 5m! Think about a professional footballer, and how fast the ball is moving once is crosses the goal line (if they score, of course!) Your number of 32m/s does seem reasonable to me.
P: 948
 Quote by fsk08 F=5,58 N Then what? This is where I am stuck. And I'm not even sure if my math and use of the equation is correct..
No, your use of the equation is not correct. You have to remember that the instantaneous drag force depends on the instantaneous velocity, not an average over time. So the drag will be causing the ball to slow down, and as the velocity decreases, the drag force will decrease as well. Essentially, you will need to model this co-dependent relationship. To be honest it's been a while since I took calculus and I don't remember off the top of my head how to do this!

Maybe someone else can help out?
Sci Advisor
P: 5,419
 Quote by KingNothing You have to remember that the instantaneous drag force depends on the instantaneous velocity, not an average over time. So the drag will be causing the ball to slow down, and as the velocity decreases, the drag force will decrease as well.
That is all true, but not necessarily relevant to getting a reasonable answer.

I agree with your 5N force.

You can then say

Deceleration = force/mass = 5 / 0.44 = 11 m/s^2

So in 0.16 seconds the ball will decelerate about 0.16 x 11 = 1.8 m/s

Or from 31 m/s to 29.2 m/s

The change in the drag force will be 29.2^2 / 31^2 = 0.89 so the change in velocity will be somwhere between 1.8 and 1.8 x 0.89 = 1.6 m/s

None of the above is accurate enough to bother about a difference of 0.2 m/s in the answer (you are ignoring the fact that the ball is probably spinning, for example), so you might as well assume the force is constant.

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