Using Vectors to Measure the
Height of the Clock Tower
10/3/2016
Todd Hecker
Partners: Troy Hernandez
Background:
A vector is a quantity which has both magnitude and direction. In a two-dimensional space, the magnitude and direction
determine the horizontal and vertical components of the vector. Any two of these values can be used to find the other
two…for example, given the horizontal and vertical components of a vector, one can use simple trigonometry to calculate
the magnitude and direction of the vector.
Purpose:
Grosse Pointe South High School is a historic building. Constructed in 1928, its distinctive clock tower, well over 100
feet tall, is among the most iconic features of any school in the metro Detroit area. In this lab, we attempted to use the
concept of vectors to calculate the height of Grosse Pointe South High School’s clock tower.
Hypothesis:
We claim that the height of the clock tower can be calculated, using vectors and some rudimentary measurements, to
within 10% of its actual height.
Materials:

Clinometer

Tape measure
Procedure:
Our general process was, for each trial, to use three measurements to calculate the height of the tower:
 The distance, h0, when standing, from Mr. Hecker’s eye to the ground
 The distance, d, Mr. Hecker stood from the base of the tower
 Our measured angle of elevation, θ, to the top of the tower
1. To measure the distance from Mr. Hecker’s eye to the ground, we had Mr. Hecker stand up straight and then used two
meter-sticks to measure the distance. Sliding the top meter stick up the bottom meter stick allowed us to get a
reasonably accurate measurement.
2. Measuring the distance from Mr. Hecker to the base of the tower:
a. Unfortunately, we did not have a device which would accurately measure distances that were big enough for
our needs. So, we measured the length of a hallway, and then counted how many steps it took to walk down
the hallway. This provided us with a conversion factor which allowed to convert from distance units of
“steps” to distance units of “meters.”
b. We then stood at the base of the tower and
walked, in a straight line, a given number of
steps away from the base. We then used our
conversion factor to convert this to meters.
3. To measure the angle of elevation:
a. Mr. Hecker stood straight up, at the location
described in step 2, and looked through the
clinometer at the top of the tower.
b. Once the pendulum on the clinometer had
stopped swaying, Mr. Hernandez recorded the
angle.
4. Given this data, we were able to calculate the height of
the tower, which can be seen in the drawing to be h0 +
h1. See the “Graphs and Data” section for more
*Note: Diagrams may be drawn in by hand. 
detailed calculations.
Graphs and Data:
Measured length of hallway: 67.4 m
Number of steps to walk hallway: 72
Trial
Measured
distance
from clock
tower
Measured
angle from
clinometer
Your height
Calculated height of clock
tower
1
26 steps
48o
5’ 10”
27.8 m
2
40 steps
42o
5’ 10”
35.5 m
3
57 steps
35o
5’ 10”
39.1 m
5’ 10”
34.1 m
Avg.
height
Conclusion:
1. Trial 1 calculations:
Sample calculation of ho:
Sample calculation of d:
Sample calculation of h1:
Sample calculation of tower height:
2. Percent Error:
3. Possible sources of error:
a. We were unable to measure d to a point DIRECTLY under the peak of the tower
b. Our measuring device (walking) depended on us always taking the same size steps
c. The ground in the yard may not have been horizontal
d. The clinometer only had markings for each 15o thus our angle measurement was not very precise
4. Uncertainty:
OTHER NOTES ABOUT LABS:




Use font size 10 – 12
Use single or double spacing
If you need pages with graphs to be in landscape, that is acceptable, but all pages which are mostly text should be
in portrait.
ALL WRITING MUST BE IN YOUR WORDS…You may discuss ideas with your group, but then write it in
your own words. Changing