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Display some collected data which clearly support your answer and discuss how your data provides support for your answer.
Display some collected data which clearly support your answer and discuss how your data provides support for your answer.
Display some collected data which clearly support your answer and discuss how your data provides support for your answer.
perform quick calculations to determine:the time required for the boat to reach the opposite bank (of a 100-meter wide river) and the distance that the boat will be carried downstream by the current. Use the simulation to check your answer(s).
The river is 80 meters wide. The river flows south at 2 m/s.The river is 120 meters wide.The river flows south at 4 m/s.The boat heads across the river at 6 m/s.The boat heads across the river at 10 m/s.None of these affect the time to cross the river.
The boat heads across the river at 6 m/s.The river flows south at 4 m/s.The boat heads across the river at 10 m/s.None of these affect the landing location.The river flows south at 2 m/s.
Use the principles of vector addition to determine the resultant velocity vector for each combination of 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 vector.
Navigation Simulation
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:
Part 1: Becoming Familiar with the Controls
Navigate to the and experiment with the on-screen buttons in order to gain familiarity with the control of the animation, then answer the following questions.
Will a change in the speed of a current change the time required for a boat to cross a 100 m wide river?
For a constant river width and boat heading, what variable(s) affect(s) the time required to cross a river?
Suppose that a motor boat can provide a maximum speed of 7 m/s with respect to the water. What heading will minimize the time for that boat to cross a 100-m wide river? ___________
Part 2: Crossing Time - Pointing East
Run the simulation with the following combinations of boat speeds and current speeds with a heading of 0º (due East).
Before running each simulation:
12
2
12
3
12
4
20
2
20
5
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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? Explain.
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What two quantities are needed to calculate the distance the boat travels downstream?
Use what you have learned about the d-v-t relationships to solve the following problems.
A waterfall is located 180 m downstream from where the boat is launched. If the speed of the current is 3 m/s, and the boat is pointing due east, then what minimum boat speed is required to cross the 100-meter wide river before falling over the falls?
Do some rough calculations and then check your prediction using the simulation. Please describe what you have done or include a picture of your calculations below.
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Repeat the above calculations to determine the boat speed required to cross the 100-meter 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.
For the next two questions, consider a boat which begins at a point (we’ll call it point A) and heads straight across a 100-meter 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 some point (we’ll call it point C).
Which of the following would cause the boat to take more time to reach the opposite shore? Highlight all that apply.
Explain.
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Which of the following would cause the boat to reach the opposite shore at a location SOUTH of C? Highlight all that apply.
Explain.
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Observe that the resultant velocity vector (v or vBE) is the vector sum of the boat velocity (vyor vBW) and the river velocity (vx or vWE).
Boat Velocity
Current Velocity
15 m/s [E]
4 m/s [S]
20 m/s [E]
5 m/s [S]
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Conclusion:
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
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