Purpose:
The purpose of this activity is to analyze the
relationship between the two vector components of motion
for a river boat as it travels across a river in the
presence of a current.
Procedure and
Questions:
1. Navigate to the Riverboat
Simulator page and experiment with the onscreen
buttons in order to gain familiarity with the control of
the animation. The width of the river, speed of the
river, speed of the boat, and direction (or heading) of
the boat can be modified. The animation can be started,
paused, continued, singlestepped or rewound.
After gaining familiarity with the program, use it to
answer the following questions:
2. Will a change in the speed of a current change the
time required for a boat to cross a 100 m wide river?
_________ In the space below, display some collected
data which clearly support your answer. Discuss how your
data provide support for your answer.
3. For a constant river width and boat heading, what
variable(s) effects the time required to corss a 100 m
wide river? __________________________ In the space
below, display some collected data which support your
answer. Discuss how your data provide support for your
answer.
4. Suppose that a motor boat can provide a maximum
speed of 10 m/s with respect to the water. What heading
will minimize the time for that boat to cross a 100m
wide river? ___________ In the space below, display some
collected data which clearly support your answer. If
necessary, discuss how your data provide support for your
answer.
4. Run the simulation with the following combinations
of boat speeds and current speeds with a heading of 0
degrees (due East). Before running each simulation,
perform quick calculations to determine the time required
for the boat to reach the opposite bank (of a 100meter
wide river) and the distance that the boat will be
carried downstream by the current. Use the simulation to
check your answer(s).
Boat
Speed
(m/s)

Current Speed
(m/s)

Time to Cross
River
(s)

Distance
Downstream
(m)

12

2



12

3



12

4



20

2



20

5



5. Study the results of your calculations in the table
above and answer the following two questions.
 What feature in the table above is capable of
changing the time required for the boat to reach the
opposite bank of a 100meter wide river? Explain.
 What two quantities are needed to calculate the
distance the boat travels downstream?
6. Use what you have learned from the
distancespeedtime relationships to solve the following
two problems.
A waterfall is located 45.0 m downstream from
where the boat is launched. If the current speed is 3
m/s, then what minimum boat speed is required to cross
the 100meter wide river before falling over the
falls? Show your calculations and then check your
prediction using the simulation.
Repeat the above calculations to determine the boat
speed required to cross the 100meter wide river in
time if the current speed was 5 m/s and the waterfall
was located 45.0 m downstream. Again, check your
predictions using the simulation. PSYW
For
Questions 7 and 8: Consider a boat which begins at
point A and heads straight across a 100meter wide
river with a speed of 8 m/s (relative to the water). The
river water flows south at a speed of 3 m/s (relative to
the shore). The boat reaches the opposite shore at point
C.
7. Which of the following would cause the boat
to reach the opposite shore in MORE time? List all that
apply in alphabetical order with no spaces between
letters.
a. The river is 80 meters wide.
b. The river is 120 meters wide.
c. The boat heads across the river at 6 m/s.
d. The boat heads across the river at 10 m/s.
e. The river flows south at 2 m/s.
f. The river flows south at 4 m/s.
g. Nonsense! None of these effect the time to
cross the river.
8. Which of the following would cause the boat to
reach the opposite shore at a location SOUTH of C? List
all that apply in alphabetical order with no spaces
between letters.
a. The boat heads across the river at 6 m/s.
b. The boat heads across the river at 10 m/s.
c. The river flows south at 2 m/s.
d. The river flows south at 4 m/s.
e. Nonsense! None of these effect the location
where the boat lands.
9. Observe that the resultant velocity
(v) is the vector sum
of the boat velocity
(v_{x}) and
the river velocity
(v_{y}). Use
the principles of vector addition to determine the
resultant velocity for each combination of boat/current
velocities listed below. Use a sketch of the two vectors
and the resultant accompanied by the use of the
Pythagorean theorem and trigonometric functions to
determine the magnitude and direction of the resultant.
PSYW
Boat Velocity = 15 m/s,
East
Current Velocity = 4 m/s, South

Boat Velocity = 20 m/s,
East
Current Velocity = 5 m/s, South



v_{resultant}
Magnitude: ___________________ m/s
Direction: ________________

v_{resultant}
Magnitude: ___________________ m/s
Direction: ________________

For the two sets of boat and current velocities listed
above, use the Pythagorean theorem to calculate the
resultant displacement of the boat in order to cross the
190meter wide river. Show your calculations for each
case in the space below.
Boat Velocity = 15 m/s,
East
Current Velocity = 4 m/s, South
d_{across} = 190 m

Boat Velocity = 20 m/s,
East
Current Velocity = 5 m/s, South
d_{across} = 190 m

d_{downstream} = _____________
d_{resultant} =
_____________

d_{downstream} = _____________
d_{resultant} =
_____________

Summary Statement:
It is often said that "perpendicular components of
motion are independent of each other." Explain the
meaning of this statement and apply it to the motion of a
river boat in the presence of a current.