Crossing the River Discussion Created for CVCA Physics

Crossing the River Discussion Created for CVCA Physics by Dick Heckathorn 15 October 2 K+4

Q-1 Problem 1 Heading downstream (w/current) v = ? Q-2 Heading upstream (against current) V=? Q-3 What is shore doing? Q-3 a Tuber observation of boat Q-4 Heading across river (no current) v = ? Q-5 Heading across river (w/current) v = ? Q- Study the v and d vector drawings Q-6 Going directly across the river with current Quiz 1 Quiz 2 Quiz 3 Quiz 4

Problem We wish to cross a river. This unique river has a constant current of 6 m/s from bank to bank. Speed of the Current 6 m/s

We will be crossing in a boat that can travel with a speed of 8 m/s in still water. (This means that the boat will have this speed in the direction that the boat is pointing. ) Speed of the boat 8 m/s

Question 1 Heading Downstream If the boat is heading downstream, what will be the resultant speed of the boat as seen from shore? VC = 6 m/s VB = 8 m/s VR = 14 m/s

Question 2 Heading Upstream If the boat is heading upstream, what will be the resultant speed of the boat as seen from shore? VR = 2 m/s VC = 6 m/s VB = 8 m/s

Question 3 Changing to Boat Reference Frame How fast will a person in the boat see the shore pass by? At the same speed that the person on shore sees the boat pass by - but - in the opposite direction.

Question 3 a Changing To Tuber Reference Frame How fast will a tuber drifting with the water see the water pass by? The tuber will be floating with the water. Thus they will say the speed of the water relative to them is zero.

Question 3 a Changing Reference Frame How fast will a tuber see the boat go by? VB+C = 14 m/s VB = 8 m/s - VC = 6 m/s

Question 3 a Changing Reference Frame What is the new velocity of the boat? Has the velocity of the boat changed? I trust you said no. Thus the tuber always sees the boat traveling at a speed of 8 m/s and. . . with a velocity of 8 m/s in the direction it is heading. (downstream)

Problem 4 Heading Across - No Current The river has no current. We will now head (in the boat) across the river which is 120 m wide.

Problem 4 Heading Across - No Current VB = 8 m/s he velocity of the boat is: d. A = 120 m he crossing displacement is: Note…Both must have different scales!

Problem 4 Heading Across - No Current VB = 8 m/s We know : d. A = 120 m How long will it take to cross the river?

Problem 5 Heading Across - With Current Now lets turn the current back on and head directly across the river. What will be the resultant velocity of the boat?

Problem 5 Heading Across - With Current across 36. 9 o downstream /s 0 m =1 R 36. 9 o V 10 m/s VC = 6 m/s VB = 8 m/s Finally, Then Next, First draw find the the Next add magnitude angle the velocity resultant . vector of current the vector of the resultant: boat. vector. Thus the resultant velocity of the boat is

Problem 5 Heading Across - With Current /s 0 m =1 R V Which v ? 10 m/s VB = 8 m/s d = 120 m How long will it take to cross the river? We know that: VC = 6 m/s

Problem 5 Heading Across - With Current Nice try… but 12 sec is incorrect. Why? Where do we go from here? We Thus have when learned we divide that a vector times by a vector, a scalarthey results bothinmust a vector be with in thethe same direction as the original vector.

Problem 5 Heading Across - With Current 0 m =1 R V Which v ? 8 m/s /s VC = 6 m/s VB = 8 m/s d = 120 m We know that:

Problem 5 Heading Across - With Current Are you surprised that the time (15 sec) to cross the river heading at right angle to the current is the same time that it took to cross the river with no current? (15 sec)?

Problem 5 Heading Across - With Current If so, remember that the current is at right angles to the direction you are heading. Thus the current has no affect on the crossing speed or the crossing time.

Problem 5 Heading Across - With Current How far downstream will we be when we reach the other shore? What time which velocity The This one equation thatand is in relates the same distance direction to use? aswill velocity thewe displacement and time. which we want to find.

Problem 5 Heading Across - With Current And the answer is: VC = 6 m/s t = 15 s

Study The Following d R =1 50 m d. D = 90 m d. A = 120 m /s =1 0 m v. R v. B = 8 m/s Vc = 6 m/s Thus different scales must be used for Each vector ontriangle the right equal totimes the They are completely different How does the onisathe right They are similar triangles: vector the velocity and the displacement. on leftone multiplied bydirection. 15 sec. vectors. compare tovector the on the left? avector scalar = athe in the same

Problem 6 Going Directly Across with Current At what direction must one head so that we will reach the shore directly across the river from where we started?

Problem 6 Going Directly Across with Current We know the following: VC = 6 m/s Speed of boat = 8 m/s Direction we wish to go.

Problem 6 Going Directly Across with Current We Then Finally, First, Nextproceed add draw add athe dotted as thefollows: V = 6 m/s C speed two the linecurrent vectors. indicating of the boat the V with velocity direction its head of the at the B = 8 tail vector. resultant of the velocity. current m /s and its tail on the resultant direction.

Problem 6 Going Directly Across with Current What We can trig use thethe side Nexthave we do will you need Did you guess ofunction opposite sine can and we the to think to find the 36. 9 ? angle Sorry ? find ? angle use hypotenuse. find tothe . is? direction the boat ? will Thathead? is not the correct answer? VC = 6 m/s V B = 8 m /s

Problem 6 Going Directly Across with Current We will useneed Finally we The resultant pythagorean to findofthe speed the boat theorem: resultant speed of is the boat. VC = 6 m/s V B = 8 m /s

Problem 6 Going Directly Across with Current The Or Giving we resultant velocity could the result of use velocity the of: current vaddof the is boat computer is program. VC = 6 m/s V B = 8 m /s = 5. 83 m/s 90 o

Problem 6 Going Directly Across with Current The resultant velocity of the boat is: VC = 6 m/s V B = 8 across, 48. 6 o upstream m /s

Quiz Question 1 A boat heads directly across a river 41 m wide at 3. 8 m/s. The current is 2. 2 m/s. a. What is resultant velocity of the boat? b. How long to cross the river? c. How far downstream is boat when it reaches the other side?

Quiz Question 1 Answers a. 4. 39 m/s across 30. 1 o downstream b. 10. 8 sec c. 23. 7 m

d R = d. D = d. A = 41 m R = VC = 2. 2 m/s V VB = 3. 8 m/s Quiz Question 1 Answers (not to scale)

Quiz Question 2 A boat heads directly across a river 187 m wide at 10. 3 m/s. The current is 6. 7 m/s. a. What is resultant velocity of the boat? b. How long to cross the river? c. How far downstream is boat when it reaches the other side?

Quiz Question 2 Answers a. 12. 3 m/s across 33. 0 o downstream b. 18. 2 sec c. 121. 9 m

d R = d. D = d. A = 187 m R = VC = 6. 7 m/s V VB = 10. 3 m/s Quiz Question 2 Answers (not to scale)

Quiz Question 3 A boat heads directly across a river 110 m wide at 8. 5 m/s. The current is 3. 8 m/s. a. What is resultant velocity of the boat? b. How long to cross the river? c. How far downstream is boat when it reaches the other side?

Quiz Question 3 A boat heads directly across a river 110 m wide at 8. 5 m/s. The current is 3. 8 m/s. d. At what angle will the boat head so that it will go directly across? e. What will be the crossing speed when heading directly across? f. How long to cross?

Quiz Question 3 Answers a. 9. 31 m/s o across 24. 1 downstream b. 12. 9 sec c. 49. 2 m o d. across 26. 6 upstream f. 14. 5 sec e. 7. 60 m/s

d R = d. D = d. A = 110 m R = VC = 3. 8/s V VB = 8. 5 m/s Quiz Question 3 Answers (not to scale)

Quiz Question 4 A boat heads directly across a river 245 m wide with a speed of 14. 2 m/s. The current is 8. 3 m/s. a. What is resultant velocity of the boat? b. How long will it take the boat to cross the river? c. How far downstream is boat when it reaches the other side?

d. At what angle will the boat head so that it will go directly across? e. What will be the crossing speed when heading directly across? f. How long to cross? g. How long will it take the boat to cross the river if there is no current?

Quiz Question 4 Answers a. 16. 45 m/s o across 30. 3 downstream b. 17. 3 sec c. 143. 2 m d. across 35. 8 o upstream e. 11. 5 m/s f. 21. 3 sec g. 17. 3 sec

That’s all folks!