Knowing that it is exactly 60’ from the foul line on a bowling alley to the head pin, give me a formula to figure out ball speed in miles per hour. I throw a hook but I guess you’ll have to assume that the ball travels in a straight line. A hook would cover more than 60’.
P.S. I have a stop watch.
(40.9090…) * T[sub]seconds[/sub] = V[sub]MPH[/sub]
No problem. Here you go:
speed (mph) = distance travelled (miles) / elapsed time (hours)
So, since you know how far the ball will travel - 60 feet - all you have to do is measure the time that elapses betwen letting go of the ball and the striking of the lead pin. Your stopwatch should do this nicely. The only problem is that your measurements are in the wrong units, but we fix that like this:
1 mile = 5280 feet, so 60 feet = 60/5280 miles = .011 miles
1 hour = 3600 seconds, so x seconds (whatever the time is) = x/3600 hours
Now, just divide .011 by x/3600. In simplified form:
speed (mph) = 40.9/x
Where x is the elapsed time in seconds.
In the interest of accuracy, I should note that this is the average speed, and that the instantaneous speed doubtless varies along the way. Also, since you’re just timing by hand, the extra distance travelled by the curve should fall within the error in time measurement, so there’s no real point in trying to correct for it unless you want to set up a more accurate timer.
Obviously that should read "40.9090… / T[sub]seconds[/sub] = V[sub]MPH[/sub]. :smack:
How is that? I’m estimating (using 1 mississippi 2 mississippi) that my ball takes between 2.5 and 3 seconds to cover 60’. With that formula, that equals 122mph. I may have the strength and power of ten men, but I can’t roll a 16lb ball 122 mph.
Aahhh, I see the correction now. Thanks.
I actually can hurl a 16 lb. ball 122 mph.
But for you, you need to divide by the time elapsed, not multiply.
I give lessons, by the way…
[QUOTE=MonkeyMensch]
I actually can hurl a 16 lb. ball 122 mph.
[QUOTE]
off a cliff?
A handy rule of thumb is that speed in feet per second is approximately 1.5 times the speed in miles per hour.
So if you cover 60 feet in 2.5 seconds, that would be 24 feet per second, or about 18 mph, and 3 seconds would be 20 feet per second, or 13.3 mph. That way, you can do it in your head and not have to get out your calculator.
Since you are dealing with a relatively fast object over a relatively small distance, I would take several measurements and average them together.
If you know the time and distance travelled, the kinematic equation to use is:
d = (v0 + vf)/2 * t
Rearranging the terms a bit, we get
vf = 2d/t - v0,. where
v0 is your running speed
Urban Ranger, would you mind explaining what that equation is supposed to represent? I don’t get it. What does running speed have to do with the bowling ball?
That’s one of the Newtonian kinematic equations that you can use to figure out approximate answers for linear motions. Each of the equations involve 4 of the 5 variables (v0 - initial velocity, vf - final velocity, a - acceleration, d - distance, t - time) , you can find the forth by knowing the other 3.
You need to know the running speed because the ball isn’t being thrown from rest, there’s a running start.
Seems to be completely irrelevant to me.
It doesn’t make any difference to the ball speed whether you:
a) tossed it from a standstill
b) tossed it from a running start
c) fired it from a cannon
d) dropped it from orbit and then had it ricochet of Superman’s chest.
The ball speed is the ball speed.
Unless you’re trying to score points against MonkeyMensch or something. It’s easy enough for anyone to hurl a 16 lb ball at 122 mph if they have access to a car that can do 122 mph.
Three things come to mind:
[ul][li]The ball’s initial speed is not your running speed. I think this is what Desmostylus is saying.[/li][li]The acceleration on a rolling ball down a bowling alley is so small, I think that the uncertainty in the stopwatch would drown it out, so it’s best to set it to 0.[/li][li]Even if there were an acceleration, I think King Friday would want the average speed, which is simply given by d/t, not the final speed.[/li][/ul]
I don’t have much to add here, only that I went bowling last Saturday and they have apparently added radar guns to clock the speed of the balls. I was disappointed that the best I could do was about 20.5 mph. And I was slinging.
[/hijack]
Urban Ranger is right, you could calculate the final velocity (that is, the velocity of the ball as it strikes the lead pin) with that kinematic equation. There’s only one problem: V[sub]0[/sub] in that equation refers not to the running speed of the thrower, but rather to the speed of the ball as it leaves the thrower’s hand.
You see, in this case the kinematic equation allows us to calculate the final speed of the ball without knowing the acceleration. Think about it: as the ball travels the length of the alley it slows down due to rolling friction, so the final velocity must be less than the initial velocity. That’s what the kinematic equation tells us: the distance travelled (d) is equal to the average velocity ([v[sub]0[/sub]+V[sub]f[/sub]]/2) times elapsed time (t).
Really, it’s substantially the same as the equations above:
d = V[sub]avg[/sub]*t
leads to
V[sub]avg[/sub] = d/t
Granted, the running speed of the thrower might influence the initial speed of the ball, but the running speed isn’t an input in in the kinematic equation.
Ok, my average time was 2.63 seconds, or 15.55 mph on the strike ball. Now you can enter those numbers in your equations. (please note that the afore mentioned method of timing, 1 mississippi 2 mississippi, was pretty darn accurate)
Maybe it’s a bit late in this thread, but here is a good calculator for what you need:
http://www.1728.com/velocity.htm
It allows input in 12 units of time, distance or velocity.
Any of the posters in this thread might want to take a look.