Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.
You can change this under Settings & Account at any time.

No, thanks

The Calculus of a Marathon

No description
by

Amy Rechkemmer

on 27 May 2014

Comments (0)

Please log in to add your comment.

Report abuse

Transcript of The Calculus of a Marathon

The Calculus of Running a Marathon
design by Dóri Sirály for Prezi
Used by many runners

We know it shows location but...


how does it work?

demo

How Can Calculus Help You Win Your Marathon?


Let's Find Out!
Runner A Calculations
Global Positioning System
Runner A: a = 3 cos(x) + 1
Runner B: a = x/20

Pre-race info:
Both runners start out with a velocity of 0
Runner B oversleeps and comes late to the race, starting the race 200 meters behind the start line
And They're Off!
V = 3 sin(x) + x

X = 3 sin(x) + x dx
X = -3 cos(x) + x^2/2 + c
0 = -3 cos(0) + 0 + c
0 = -3 + c
C = 3

X = -3 cos(x) + x^2/2 +3



A = 3 cos(x) + 1

V = 3 cos(x) + 1 dx
V = 3 sin(x) + x + c

0 = 3 sin(0) + 0 + c
c = 0

V = 3 sin(x) + x

Runner B Calculations
V = 1/40 x^2

X = 1/40 x^2 dx
X = 1/120 x^3 + c
-200 = 1/120 (0)^3 + c
c = -200

X = 1/120 x^3 - 200


A = x/20

V = x/20 dx
V = 1/40 x^2 + c
0 = 1/40 (0)^2 + c
c = 0

V = 1/40 x^2

When Will Runner A Finish?
42, 195 =
-3 cos(x) + x^2/2 +3

0 = -3 cos(x) + x^2/2 – 42, 192

t = 290.49 minutes to finish the marathon

That is close to 5 hours

Marathon = 26.2 miles
26.2 mi = 42, 195 m

To find time it takes to finish the race, we can plug 42, 195 in for X and solve for (x), or time in minutes

When Will Runner B Finish?
42, 195 = 1/120 x^3 – 200

42, 395 = 1/120 x^3

t = 171.99 minutes to finish the marathon

That is close to 3 hours

Marathon = 26.2 miles
26.2 mi = 42, 195 m

To find time it takes to finish the race, we can plug 42, 195 in for X and solve for (x), or time in minutes



Full transcript