(Modeling) Measuring Rainfall Suppose that vector R models the amount of rainfall in inches and the direction it falls, and vector A models the area in square inches and the orientation of the opening of a rain gauge, as illustrated in the figure. The total volume V of water collected in the rain gauge is given by V= | R · A |. This formula calculates the volume of water collected even if the wind is blowing the rain in a slanted direction or the rain gauge is not exactly vertical. Let R = i - 2 j and A = 0.5 i + j. (a) Find | R | and | A | to the nearest tenth. Interpret the results. (b) Calculate V to the nearest tenth, and interpret this result.
(Modeling) Measuring Rainfall Suppose that vector R models the amount of rainfall in inches and the direction it falls, and vector A models the area in square inches and the orientation of the opening of a rain gauge, as illustrated in the figure. The total volume V of water collected in the rain gauge is given by V= | R · A |. This formula calculates the volume of water collected even if the wind is blowing the rain in a slanted direction or the rain gauge is not exactly vertical. Let R = i - 2 j and A = 0.5 i + j. (a) Find | R | and | A | to the nearest tenth. Interpret the results. (b) Calculate V to the nearest tenth, and interpret this result.
Solution Summary: The author explains how to calculate the dot product of vectors sqrtleft|Rright| to the nearest tenth, if R=i-2j,A
(Modeling) Measuring Rainfall Suppose that vectorR models the amount of rainfall in inches and the direction it falls, and vector A models the area in square inches and the orientation of the opening of a rain gauge, as illustrated in the figure. The total volume V of water collected in the rain gauge is given by
V= |R · A|.
This formula calculates the volume of water collected even if the wind is blowing the rain in a slanted direction or the rain gauge is not exactly vertical. Let R = i - 2j and A = 0.5i + j.
(a) Find | R | and | A | to the nearest tenth. Interpret the results.
(b) Calculate V to the nearest tenth, and interpret this result.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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