THE WHITE BOARD RIVER
PROBLEM: How does a boat travel on a river?
M ATERIALS:
Meter stick
tape
Protractor
Stopwatch
white board
1.2 m x 0.61 m
Small battery
powered car
PROCEDURE:
1. Your car will serve as the “boat” and the white board will serve as the “river”. The cars are nice but do not have a
speedometer. From the supplied equipment, how do you expect to determine the velocity of the boat and river?
2. Start with all the wheels of the “boat/car” on the white board “river”. Measure the length of the white board “river” and
record this as the “Boat” Distance. Be careful of units.
3. Mark the spot on the floor where the white board “river” starts to flow down the hallway. Choose the front or back edge
of the white board “river” as the reference point for measurement, and stay consistent. Have a student (the hydro
engineer) walk slowly at a constant speed while pulling the “river” across the floor. Measure the time it takes for the
“boat” to travel across the “river” while it is moving. Stop timing once the “boat” reaches the opposite shore. Measure
how far the white board “river” moves during the time it takes for the “boat” to cross. Complete three trials.
DATA ANALYSIS:
Trial
“Boat”
Distance
(m)
Time
(s)
“Boat” Velocity
(Distance/Time)
VB
(m/s)
DATA T ABLE
River Distance
River Velocity
(m)
(Distance/Time)
VR
(m/s)
Path Velocity
(Pythagorean)
R=( VB2 + VR2).5
Resultant
Velocity
Measured from
Vector Diagram
1
2
3
CALCULATIONS:
1. Calculate the Resultant using the Pythagorean Theorem and enter your answer in the data table above.
2. Find the angle that the boat travels relative to the shore using the equation  = tan-1 (Vboat /Vriver).
GRAPHICAL ANALYSIS: 3 VECTOR DIAGRAMS
 Using the velocity of the “boat” as one vector and the velocity of the “river” as the second vector, graphically add the
vectors for the resultant velocity of the “boat” for each of the three trials. Select an appropriate scale and graphically
add the vectors, either on the back of this sheet or on your own paper. Add vectors tip-to-tail. Enter the value for the
Resultant Velocity into the Data Table above. Include the angle calculated from above (calculation 2) for each
diagram, and properly label its location on the diagram.
QUESTIONS:
1. In trial 1, if the boat traveled in the same direction as the river, how fast would it travel?
2. In trial 2, if you wanted to stay in one place relative to the shore, what direction and how fast would the “boat” have to
travel?
3. In trial 3, if the boat traveled against the current, how fast would it travel? Would it be moving forward or backward
relative to the shore?
4. Calculate the percent difference between the measured and calculated resultants for the Path Velocity of each trial.
To do this: (Calculated is the Pythagorean calculation; measured is from the vector diagram.)
% difference 
measured  calculated
 100
measured  calculated
2