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A rowboat is traveling in the direction of θ=135∘ at 6.1 knots against a 1.1 knot current that is flowing in the direction of θ=330∘. What is the boat's actual velocity?

A. 5 knots
B. 4 knots
C. 3 knots
D. 2 knots

User GabLeRoux
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1 Answer

4 votes

Final answer:

The boat's actual velocity is 4 knots. (Option B is the correct answer).

Step-by-step explanation:

To determine the boat's actual velocity, we need to calculate the resultant velocity. We can do this by using vector addition. The boat's velocity can be represented as a vector with a magnitude of 6.1 knots and a direction of 135°. The current's velocity can be represented as a vector with a magnitude of 1.1 knots and a direction of 330°. Adding these vectors together will give us the resultant velocity.

To add the vectors, we can break them down into their x and y components using trigonometry. The x-component of the boat's velocity is 6.1 * cos(135°) = -4.31 knots. The y-component of the boat's velocity is 6.1 * sin(135°) = 4.31 knots. Similarly, the x-component of the current's velocity is 1.1 * cos(330°) = 0.95 knots, and the y-component is 1.1 * sin(330°) = -0.60 knots.

Adding the x-components and the y-components separately, we get a resultant velocity of (-4.31 + 0.95) knots in the x-direction, and (4.31 - 0.60) knots in the y-direction. Using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity as sqrt((-4.31 + 0.95)^2 + (4.31 - 0.60)^2) = 4 knots.

User SMeyers
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