Optimizing Sign Visibility: Investigating Angle Variations for Approaching Cars

[Alec]

"The lower part of a 2.0 meters high road sign is at a distance of 4.0 meters from the car drivers eyes. It's difficult to read the sign at such a distance, as well as when the distance is too short. Investigate how the angle varies when the car is approaching on a straight road. At what distance is the angle as big as possible? The sign is readable if the angle is greater than 1. Investigate for how long time the sign will be readable"

Thats the problem to solve.
Of course the time depends on how fast one is driving.
I haven't gotten anywhere with this problem.
Please help me!

 

[berkeman]

The numbers in your re-statement of the problem are hard to understand. Why would a sign be hard to read at 4m ("at such a distance")? And even closer? And what do you mean by an angle greater than 1? Do you mean 1 radian? Or 45 degrees when the tan(theta)=1?

Could you please re-check the numbers, and clarify the problem statement so we can help you better?

 

[jocke^^]

I can explain the problem better.

You got a road sign ahead. The sign is 2 meters high, The distance from the sign to the ground is 4 meters. The sign is hard to see in a big distance. It is impossible to se if the visual angle is smaller then 1 degree. (which means that he can't se the sign on a big and small distance)

You're going to examine how the angle changes when the car approaches the sign and on what distance the biggest angle is.

See picture.


//jocke

 

[Alec]

I'm sorry I was posting for a friend who had troubles registering at this forum.
He posted a reply with a picture that clarifies the setting.(above)
I just translated this from our mother tongue, thus the bad english and the obscure statement.

 

[Integral]

Here is my understanding of the problem.

By definition in the problem the sign is unreadable at 4m because you are to close. It becomes readable in the distance when it subtends 1deg.

The first thing I would do is convert the degrees to radians, since degs are not the natural unit for this type of problem.

So with:
$\Theta$ in radians
s = subtended arc length in meters
r = distance in m you have:

$$\theta = \frac s r$$

You need to find the distance at which the angle = 1deg (in radians) from there you should be able to work out the rest of the problem.

 

[jocke^^]

No the sign is readable all the time whem the "visual angel" > 1 .

4 meters is the height over the ground as you can se in the picture. Alec wrote wrong, he missunderstood the problem. The distance and the angle are what you are going to examine.

 

[Gokul43201]

jocke/alec, have you solved other problems in heights and distances ? What is the first thing you do ?

Okay, the first thing is to draw the diagram. So, what's the next step ? Is the diagram complete ? What's missing in it ?

 

[Integral]

The initial statement makes more sense then the picture. At least then you have some definition of a minimum reading distance.

How do you determine the minimum distance at which the sign can be read?

I have given you what you need to find the maximum, any distance less than that at which the sign subtends 1 deg the angle will be greater then 1 deg.

 

[Gokul43201]

Integral, if you get directly below the sign, it subtends an angle of 0 degs - so there is a minimum distance as well. If you set up the equations for the triangles, you get a quadratic equation. The two roots give you the pair of end points.

 

[jocke^^]

Thnx a lot.. you helped me out.

//Jocke