# Homework Help: Calculus derivatives word problem

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1. May 17, 2018

### robin123

1. The problem statement, all variables and given/known data
Is it possible to accurately approximate the speed of a passing car while standing in the
protected front hall of the school?
Task: Determine how fast cars are passing the front of the school. You may only go
outside to measure the distance from where you are standing to the road. All
other measurements must be taken from inside the building (I want you to stay
warm and dry!). Make sure to clearly explain your process to gauge the speed of
passing cars and submit all of your work!

2. Relevant equations
speed= distance/time

3. The attempt at a solution
time can be calculated for distance we have to suppose an angle and working with triangles but i am not able to figure out how

<Moderator's note: Approved as OP doesn't ask for a solution but just a guidance.>

Last edited by a moderator: May 17, 2018
2. May 17, 2018

### LCKurtz

Draw a section of the road and the perpendicular line from where you are standing to the road. That's the distance you know. With a surveyor's transit measure the angles to the starting and ending point where you can see the cars, and draw those two lines. Now use trigonometry and a timer.

Last edited: May 17, 2018
3. May 17, 2018

### Staff: Mentor

Or even use just your protractor from your Trigonometry class, but it won't be as accurate. For extra credit, estimate your error when using the protractor versus using a super-accurate instrument to measure the angles to the first and last positions of the cars...

4. May 17, 2018

### phinds

@robin123 a similar problem, but with one less step (no speed involved) is how would you figure out the height of a flagpole with a protractor, a long tape measure, and no ladder.

5. May 17, 2018

### robin123

will there be 2 lines with different angles? does that mean i will have two diagrams?

6. May 17, 2018

### Staff: Mentor

Just show us a sketch of your building, the road, the distance to the road, and the angles to the initial and final car positions as it passes by. Use the Upload button at the lower right of the Reply window to Upload a PDF or JPEG of your sketch.

7. May 17, 2018

### robin123

will it look like this?

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8. May 17, 2018

### LCKurtz

Yes. You could measure on the other side of the perpendicular too until the car gets out of sight. Do you know how to use trigonometry to figure out how far the car goes while it is in sight and you are timing it?

9. May 17, 2018

### robin123

yeah, I can use the trigonometry but for that other side, I need an angle. I am confused about that angle. part. For the time I will start with 0s and till the time I can see it.

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10. May 17, 2018

### LCKurtz

I would do it with two angles. The angle $\theta$ you have drawn for the car approaching the perpendicular and another angle $\alpha$ on the other side of the perpendicular as the car leaves the perpendicular. Those angles aren't zero. They are what you are going to measure so they are known.

11. May 17, 2018

### ehild

You do not need to measure angles . Measure the distance between the road and the wall, D. Stand at a distance d from the window of your room. Measure the width of the window: w. Measure the time you see the car passing in front of the window. The triangles shown are similar, so you can calculate the distance s the car travels from the measured data: D, d, and w.

12. May 17, 2018

### LCKurtz

@ehild: Aren't you assuming the building and window are parallel to the road?

13. May 18, 2018

### ehild

Yes, I assume. It is quite common, that the buildings are parallel to the road isn't it?
Otherwise the problem would be tricky to measure angles. And the distance of the road from the building would not be constant along the route of the car.

14. May 18, 2018

### robin123

i am confused that how D,d,w can help us calculate s

15. May 18, 2018

### ehild

The AOB triangle is similar to POQ triangle. What is the ratio s/w in terms of d and D?

16. May 18, 2018

### robin123

if the above two triangles are similar, that's mean s should be equal to w?

17. May 18, 2018

### ehild

NO. They are not congruent. What does similar mean in geometry?

18. May 18, 2018

### robin123

Sides are proportional

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19. May 18, 2018

### ehild

Which sides are proportional?

20. May 18, 2018

### robin123

Is that the way I am gonna find D?

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