PhysicsLAB: Indirect Measurements: Height by Measuring The Length of a Shadow

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

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.