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Mathematics Clinic => Grade 9 Mathematics => Topic started by: mydiamond on Oct 4, 2013

Title: How to calculate time in flight for a baseball pitch?
Post by: mydiamond on Oct 4, 2013

Starting speed: 89.6 mph
Ending speed: 77.7 mph
Distance travelled: 55 feet

How can I calculate the time in flight?
Is it possible to make an Excel formula so I can just plug in the numbers?

Title: How to calculate time in flight for a baseball pitch?
Post by: clippers! on Oct 4, 2013

Well, you know distance, v1, v2, and acceleration.

Try this equation:

d = t*(v2-v1)/2

Isolate for t.

Title: How to calculate time in flight for a baseball pitch?
Post by: Garrulous on Oct 4, 2013

Sure.  Start with the basic position/acceleration formula:

x= v0(t) + 1/2a(t^2)

x=55/5280 (to put it in miles), v0=89.6, and a=average acceleration = change in velocity/change in time = 11.9mph/t

pump these in the formula and you get

55/5280 = 89.6t + (5.95/t)(t^2)

55/5280= 89.6t + 5.95t

Notice that the nasty t^2 term gets taken care of by the /t you carried in from the a formula, so rearrange this to isolate t and you have your answer:

(55/5280)/(89.6+5.95)

The excel formula should look like this:

(distance in miles)/(starting speed in mph + 1/2 the change in speed in mph)  = time in hours.

I'll assume you can do the unit conversion if you want this is seconds, and since you're going to code this I won't bother to punch the calculator for you.