Fun with Numbers

A couple of word problems told at Longbottom Coffeehouse today. The videos are not directly related to the text. 

Medicine

Skills Video: Programming an IV Pump
Student Nursing Organization at UNH

A nurse needs to administer 115 milligrams of a medicine intravenously over a period of 75 minutes. The medicine will be administered through a hypodermic needle via an IV line using a calibrated pump. The pump wants the rate in milligrams per hour. What do you set the dial to?

The problem can be taken as a proportion: X milligrams over 60 minutes is proportional (equal) to 115 mg over 75 minutes:

Multiply both sides by 60. 60 over 60 on the left side cancels out leaving X by itself. Notice that 60 and 75 have a common factor of 15, reduce that and you are left with 4 over 5, which is the same as .8. Multiply that by 115 and you get 88 plus 4.0 which comes out to 92. Closest setting on the pump is 88, so that's where you set it.

Driving

Acura TL 60-0 mph Braking Test
Born to Drive

You are driving down the freeway at 60 miles per hour following the car ahead of you at a distance of two seconds. (That is, you notice something by the side of the road that you can use as a marker. When the car ahead of you passes the mark, you start counting, one-thousand one, one-thousand two, until you reach that same marker.)

Trailing two seconds behind means you are 176 feet away. (60 MPH is equivalent to 88 feet per second, 88 times two is 176.) The question is - if the car you are following were to suddenly turn into a brick wall, would you be able to stop before you hit it?

For this I am going to pull out two of my favorite formulas:

• V = AT (Velocity equals Acceleration times Time)
• D = (1/2)AT^2 (Distance equals one-half times Acceleration times Time squared)

We know the Velocity (88 FPS) and the Distance (176 Feet). Will this be enough to solve this equation? 

Substituting Velocity for AT in the second equation will give us	D = (1/2)VT
Substituting what we know for Velocity and Distance we get	176 = (1/2)88T
Multiply	176 = 44T
Divide both sides by 44:	4 = T

So if we can brake to a stop within four seconds, we will not hit the wall, the brand new wall that just suddenly appeared in the middle of the freeway.

Okay, how much strain is that going to cause? And will our car be able to do that?

Go back to our old friend V=AT and plug in our Time and Velocity and solve for Acceleration, we find that we need to slow down at a rate of 22 feet per second per second, which is like two-thirds of one gravity, so it might be possible. A race car would certainly be able to do, but how about my Korean sedan? Google says:

When it comes to the 2008 Hyundai Sonata's braking distance, specifically from 60 mph, Edmunds review indicates it is quite good for its class, coming in at less than 130 feet.

So we should be good, assuming we are paying attention, our reactions are on a hair trigger, the road surface is free of any kind of friction reducing substances, like ice, oil, dust or debris. So, in the real world, if you wake up and get your brake applied in time, you will probably hit the wall, but you probably wouldn't die in this completely fictional situation.