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Suppose you are about to cross a river with a small motor boat. The river current is moving 5 meters/minute, and the slow boat will go 10 meters/min. You want to travel perpendicular to the flow of the river (dotted line) and land at a spot directly across from where you start (at the X). Our goal is to find the vector that will tell us what direction to point our boat in so that we head straight across. 5 m/min We set up a standard coordinate system. The origin will be the where the boat launches from and the near shore will be the x-axis. We will measure angles in the standard way. Let v = < a, b > be the vector that represents the velocity the boat's motor is trying to push the boat.. Note, v = 10 m/min, the speed of the boat. Also note that is not the actual direction the boat moves because the flow of the river afafects its movement, along with its motor.
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Transcribed Image Text:Suppose you are about to cross a river with a small motor boat. The river current is moving 5 meters/minute, and the slow boat will go 10 meters/min. You want to travel perpendicular to the flow of the river (dotted line) and land at a spot directly across from where you start (at the X). Our goal is to find the vector that will tell us what direction to point our boat in so that we head straight across. 5 m/min We set up a standard coordinate system. The origin will be the where the boat launches from and the near shore will be the x-axis. We will measure angles in the standard way. Let v = < a, b > be the vector that represents the velocity the boat's motor is trying to push the boat.. Note, v = 10 m/min, the speed of the boat. Also note that is not the actual direction the boat moves because the flow of the river afafects its movement, along with its motor.
a. Letr be the vector representing the velocity of the water, which is flowing to the left at 5 m/min. Writer in component form (r= < x, y >). b. The velocity the boat will actually travel with is given by + + v. We want this new vector to point straight across the river. Use this to determine a, the x component of v. (Hint: what should the x component of 7 + v be?) c. Now, determine b, the y component of v. (Hint: recall that the magnitude of is equal to the speed the boat will travel.) d. What is the magnitude of r + v?
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Transcribed Image Text:a. Letr be the vector representing the velocity of the water, which is flowing to the left at 5 m/min. Writer in component form (r= < x, y >). b. The velocity the boat will actually travel with is given by + + v. We want this new vector to point straight across the river. Use this to determine a, the x component of v. (Hint: what should the x component of 7 + v be?) c. Now, determine b, the y component of v. (Hint: recall that the magnitude of is equal to the speed the boat will travel.) d. What is the magnitude of r + v?
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