Stopping distance, Book is wrong?

[Oz123]

Homework Statement

Tests reveal that a normal driver takes about 0.75 s before he or she can react to a situation to avoid a collision. It takes about 3 s for a driver having 0.1% alcohol in his system to do the same. If such drivers are traveling on a straight road at 30 mph (44 ft/s) and their cars can decelerate at 2 ft/s2, determine the shortest stopping distance d for each from the moment they see the pedestrians. Moral: If you must drink, please don’t drive!

Homework Equations

s=vt
y² = y² + 2ac (s - s0)

The Attempt at a Solution

I already know how the book solves it, the problem is that I'm not sure if the book is correct. Here's the solution from the book (12-15):
http://image.slidesharecdn.com/solutionmanualhibbelerengineeringmechanics12thedition-130719121523-phpapp02-131228081729-phpapp02/95/solutionmanualhibbelerengineeringmechanics12thedition-10-638.jpg?cb=1388219005 [Broken]
But the problem is that I think they gave the distance d relative to some coordinate where s=0 at t=0 and not the d that is illustrated. I think that the proper solution for this is something like this:
let the distance they got at time t=0.75s be d1=33ft and the solution they obtain is d2=517ft. Now this are relative to the origin s=0, t=0. So the distance that we want to find "d" is d=d2-d1=484ft. Same procedure for the 2nd case. Am I right?...I think the illustration is for the breaking distance, isn't it?

 

[haruspex]

But the problem is that I think they gave the distance d relative to some coordinate where s=0 at t=0 and not the d that is illustrated. I think that the proper solution for this is something like this:
let the distance they got at time t=0.75s be d1=33ft and the solution they obtain is d2=517ft. Now this are relative to the origin s=0, t=0. So the distance that we want to find "d" is d=d2-d1=484ft. Same procedure for the 2nd case. Am I right?...I think the illustration is for the breaking distance, isn't it?

I'm not grasping your difficulty with the book solution.
The idea is to calculate stopping distance, which is the sum of thinking distance and braking distance.
The book applies the formula v_f²-v_i²=2as_brake. But it substitutes s_brake=s_stop-s_think.

 

[Oz123]

Hm...ok I just reread the question and I think I get it now. So the illustration shows the distance at the time I see the pedestrian relative to the pedestrian...I.e. the distance from when t=0 to the distance when v=0. I thought that illustration was showing the distance at time t=0.75 to the distance when v=0, which is the braking time.

 

[Oz123]

sorry about this question.

 

[gneill]

Please don't drink and derive