VELOCITY VECTORS

SPTC 1

Technology-Rich Transportation Engineering Experiences

Louisiana Tech University

Activity 1• Background

• Practice using technology

• Collect data

• -> Lunch

• Analyze data

SPTC 2

Learning Objectives/Standards• CCSS.Math.Content.HSN.VM.A.1

(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).

• CCSS.Math.Content.HSN.VM.A.3(+) Solve problems involving velocity and other quantities that can be represented by vectors.

• CCSS.Math.Content.HSG.SRT.C.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

• CCSS.Math.Content.HSG.SRT.D.11(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

SPTC 3

Problem Statement• Transportation engineers often need to measure the speed

with which people drive on a particular segment of road.

• Radar guns can be used for this purpose, but they only measure the speed at which a car approaches the gun.

• How can a transportation engineer safely determine the true speed?

SPTC 4

BackgroundRadar uses the change in frequency of the radio pulse that bounces back (Doppler effect).

SPTC 5

Brain, Marshall. "How Radar Works" 01 April 2000. HowStuffWorks.com.

<http://science.howstuffworks.com/radar.htm> 07 July 2015.

You will need• Radar guns

• Measuring tape

• A non-busy road

• Sidewalk chalk or flag markers

• A driver and vehicle

SPTC 6

Get your radar gun ready• Load batteries

• Practice switching between MPH and KPH

• See how fast you can run/throw

SPTC 7

Identify your driver and route

SPTC 8

We’ll use a 10 x 10 grid to choose positions -

• Once we get out there, make sure you record your position

SPTC 9

10 ft

10 ft

10 ft 10 ft 10 ft

10 ft

10 ft 10 ft 10 ft

Back Inside• How fast was the vehicle going?

• Why did you all get different speeds?

• Is there any pattern to your answers?

SPTC 10

Let’s figure out the angle

• Side a = ____

• Side b = ____

• Angle C = ____

SPTC 11

Law of Cosines

• Side c = _____

SPTC 12

2 2 22 cos( )a b ab C c

Now we can find A using Law of Sines

• Angle A = ____

SPTC 13

sin sin sinA B C

a b c

Repeat the process to find the angle you measured from• Side a = ____

• Side b = ____

• Angle C = ____

• Side c = _____

• Angle A = ____

SPTC 14

SPTC 15

SPTC 16

SPTC 17

cosm

Av

Discussion• Are your answers more similar than before?

• Are they exactly the same? Why might that be?

• Whose measurements were the most accurate?

• Whose were the least accurate?

• What advice would you give someone trying to measure speed using a radar gun?

SPTC 18

Now what velocity do you think the vehicle was going?

SPTC 19