Calculating Minimum Distance for Safe Overtaking in a Kinematics Problem

[Scrooble]

Homework Statement

Suppose that a woman driving a Mercedes zooms out of a darkened tunnel at 30.3 m/s. She is momentarily blinded by the sunshine. When she recovers, she sees that she is fast overtaking a camper ahead in her lane moving at the slower speed of 13.7 m/s. She hits the brakes as fast as she can (her reaction time is 0.34 s). If she can decelerate at 2.9 m/s², what is the minimum distance between the driver and the camper when she first sees it so that they do not collide? (Note that she decelerates to 13.7 m/s)

Homework Equations

The Attempt at a Solution

30.3*0.34 = 10.3 m

And I can't do the rest. I've tried 5 different approaches with different answers and still got it wrong. I don't exactly understand how to do the question. All help is appreciated.

 

[mishek]

Under which condition woman won't collide with a camper ahead of her?

 

[Scrooble]

I believe that it's saying that the woman gets as close to the truck as she can without "touching" it, if that makes sense.

 

[mishek]

Well, I would say yes, but I would also say that she has to drive as fast as that camper ahead of her that she don't hit it.

 

[Scrooble]

All we were given were the problem and the equations. He never specified anything else.

 

[mishek]

Ask yourself this: In what situation you don't collide with the vehicle ahead of you?

If you drive at the same speed you won't catch up with him. Right?

Try the calculate the time needed that woman achieves the same speed as the camper.

 

[Scrooble]

Should take her approximately 5.72 seconds to match the camper's speed.

 

[mishek]

That is what I also get. Now you can calculate the distance that she would travel during that time.

 

[Scrooble]

220.8 meters

 

[mishek]

:). Not quite. I think that you have used correct formula (first in first line on your attached photo). Why did you use + sign for acceleration?

 

[Scrooble]

Sorry, I assumed that the acceleration was positive since I thought that that would be the correct perspective. So I guess the correct distance would be 125.8 m

 

[mishek]

Yes, that would be the distance needed that the lady needs to slow down to the same speed as the car ahead of her since she starts breaking. But her reaction time is 0.34 sec. During that time, i.e. before she starts breaking, she travels additional 10.3 m that you calculated at the beginning. So total distance would be enlarged for that amount.

 

[Scrooble]

Still got the question wrong somehow. My classmates are also having trouble getting the right answer, so my teacher might have made a mistake. Thank you for clarifying how to do this problem, though. It was really helpful :)

 

[mishek]

What is the right answer?

 

[Scrooble]

I'll get that to you tomorrow once I see him again.

 

[mishek]

Is the right answer perhaps 58.01 m?