!!!!!!!!!HELP!!!!!!!!!!

A boat traveling with a velocity measured in meters per second is described by the vector b= (-4,3) . In two or more complete sentences explain how to find the speed of the boat and the direction it is traveling in standard position. In your final answer, include all of your calculations.

Question

21-02-2024
Mathematics

contestada

!!!!!!!!!HELP!!!!!!!!!!

A boat traveling with a velocity measured in meters per second is described by the vector b= (-4,3) . In two or more complete sentences explain how to find the speed of the boat and the direction it is traveling in standard position. In your final answer, include all of your calculations.

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Nytex Nytex · Answer 1 · 2024-02-21T17:53:16+01:00

143.13

To find the speed of the boat, use the formula for magnitude of a vector: speed = sqrt((-4)^2 + (3)^2) = sqrt(16 + 9) = sqrt(25) = 5 m/s. To determine the direction, calculate the angle theta using arctan(3/-4) = arctan(-0.75) ≈ -36.87 degrees. However, in standard position, the angle is 180 - 36.87 = 143.13 degrees clockwise from the positive x-axis. Therefore, the boat is traveling at a speed of 5 m/s in the direction of approximately 143.13 degrees clockwise from the positive x-axis.

Brainliest always appreciated.