Lab
Indirect Measurements: Height by Measuring The Length of a Shadow
Printer Friendly Version
In this lab, you will be measuring the heights of your group members using the altitude angle of the sun and the length of the person's shadow. Each measurement will have to include the time at which it was taken since the sun's position in the sky changes throughout each day.
The mathematics behind calculating the height of the person in the above diagram is the use of the trig function tangent. In any right triangle the function tan
q
is equal to the ratio of (the length of the opposite side of the triangle) divided by (the length of the adjacent side of the triangle).
In our scenario, tan
q
= height/shadow.
So, our only question remains what is the angle of elevation of the sun? You can get that answer by consulting the website
www.susdesign.com/sunangle/
and inputting your zip code and time of day that the shadow was measured. For example the data for Daytona Beach at 11:15 in the morning of July 21, 2012 was:
Now, you will go outside and measure the lengths of the shadows of your group members. Make sure that each person stands "up tall" so that his/her shadow is correctly representing their height. You will also need to record the time at which your take each measurement. When you return to the classroom you will also need to measure the actual height of each group member while standing up straight against a wall.
To see how well both of your measurements agree, you will calculate a percent error for each member's height. The formula to do this is:
Refer to the following information for the next five questions.
In the data table below, express all length measurements in meters and remember to write out each date - August 10 NOT 8/10 (no slashes). You do not need to include the degree sign, º. Remember to go to the
SunAngle website
to obtain the correct angle for the date, time, and zip code for which you took your data.
trial
member's name
date
time of measurement
length of shadow
sun's angle
actual height
% error
1
2
3
4
5
Refer to the following information for the next two questions.
As your conclusion, calculate the answers to the following two problems. For each problem draw a diagram and label the information given. Show all of your work and turn in your calculations with your lab data sheets.
1. While taking a tour of a museum, a mother and her elementary-school age daughter noticed that the lengths of their shadows directly matched the lengths of two displays. The mother's shadow fell on a display that was 87 cm long while the daughter's shadow matched the length of a 58-cm long display. If the mother was 150 cm tall, what was the daughter's actual height?
2. The flag pole at a post office is 15 meters tall. One day, at 5 PM, the length of its shadow was 8 meters. Calculate the sun's angle of elevation at the moment the shadow was measured.
Related Documents
Lab:
Labs -
2-Meter Stick Readings
Labs -
Acceleration Down an Inclined Plane
Labs -
Addition of Forces
Labs -
Circumference and Diameter
Labs -
Cookie Sale Problem
Labs -
Density of a Paper Clip
Labs -
Determining the Distance to the Moon
Labs -
Determining the Distance to the Sun
Labs -
Eratosthenes' Measure of the Earth's Circumference
Labs -
Force Table - Force Vectors in Equilibrium
Labs -
Home to School
Labs -
Indirect Measures: Inscribed Circles
Labs -
Inertial Mass
Labs -
Introductory Simple Pendulums
Labs -
Lab: Rectangle Measurements
Labs -
Lab: Triangle Measurements
Labs -
Marble Tube Launcher
Labs -
Quantized Mass
Labs -
The Size of the Moon
Labs -
The Size of the Sun
Labs -
Video Lab: Falling Coffee Filters
Resource Lesson:
RL -
Basic Trigonometry
RL -
Basic Trigonometry Table
RL -
Curve Fitting Patterns
RL -
Dimensional Analysis
RL -
Linear Regression and Data Analysis Methods
RL -
Metric Prefixes, Scientific Notation, and Conversions
RL -
Metric System Definitions
RL -
Metric Units of Measurement
RL -
Potential Energy Functions
RL -
Properties of Lines
RL -
Properties of Vectors
RL -
Significant Figures and Scientific Notation
RL -
Vector Resultants: Average Velocity
RL -
Vectors and Scalars
Review:
REV -
Honors Review: Waves and Introductory Skills
REV -
Physics I Review: Waves and Introductory Skills
REV -
Test #1: APC Review Sheet
Worksheet:
APP -
Puppy Love
APP -
The Dognapping
APP -
The Pool Game
APP -
War Games
CP -
Inverse Square Relationships
CP -
Sailboats: A Vector Application
CP -
Satellites: Circular and Elliptical
CP -
Tensions and Equilibrium
CP -
Vectors and Components
CP -
Vectors and Resultants
CP -
Vectors and the Parallelogram Rule
WS -
Calculating Vector Resultants
WS -
Circumference vs Diameter Lab Review
WS -
Data Analysis #1
WS -
Data Analysis #2
WS -
Data Analysis #3
WS -
Data Analysis #4
WS -
Data Analysis #5
WS -
Data Analysis #6
WS -
Data Analysis #7
WS -
Data Analysis #8
WS -
Density of a Paper Clip Lab Review
WS -
Dimensional Analysis
WS -
Frames of Reference
WS -
Graphical Relationships and Curve Fitting
WS -
Indirect Measures
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
Mastery Review: Introductory Labs
WS -
Metric Conversions #1
WS -
Metric Conversions #2
WS -
Metric Conversions #3
WS -
Metric Conversions #4
WS -
Properties of Lines #1
WS -
Properties of Lines #2
WS -
Scientific Notation
WS -
Significant Figures and Scientific Notation
TB -
Working with Vectors
TB -
Working with Vectors
REV -
Math Pretest for Physics I
Copyright © 2007-2023
William A. Hilburn
All rights reserved.