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julia-pushkina [17]
3 years ago
13

A kayakeris paddling 2.50 m/s at an angle of 45° (northeast) and the current is moving 1.25 m/s at an angle of 315° (southeast).

What is the kayaker's total velocity?​
Physics
1 answer:
PIT_PIT [208]3 years ago
5 0

The kayaker has velocity vector

<em>v</em> = (2.50 m/s) (cos(45º) <em>i</em> + sin(45º) <em>j</em> )

<em>v</em> ≈ (1.77 m/s) (<em>i</em> + <em>j</em> )

and the current has velocity vector

<em>w</em> = (1.25 m/s) (cos(315º) <em>i</em> + sin(315º) <em>j</em> )

<em>w</em> ≈ (0.884 m/s) (<em>i</em> - <em>j</em> )

The kayaker's total velocity is the sum of these:

<em>v</em> + <em>w</em> ≈ (2.65 m/s) <em>i</em> + (0.884 m/s) <em>j</em>

That is, the kayaker has a velocity of about ||<em>v</em> + <em>w</em>|| ≈ 2.80 m/s in a direction <em>θ</em> such that

tan(<em>θ</em>) = (0.884 m/s) / (2.65 m/s)   →   <em>θ</em> ≈ 18.4º

or about 18.4º north of east.

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Answer:

The distance it has traveled is 3,050 m and the magnitude of its displacement is 650 m north.

Explanation:

Distance refers to the length between any two points in space, while displacement refers to the distance from a start position to an end position regardless of the path.

In other words, distance refers to how much space an object travels during its movement; is the quantity moved. It is also said to be the sum of the distances traveled. The distance traveled by a mobile is the length of its trajectory and it is a scalar quantity. In this case, the distance is calculated as:

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Displacement refers to the distance and direction of the final position from the initial position of an object. The displacement effected is a vector quantity. The vector representing the displacement has its origin in the initial position, its end in the final position, and its module is the distance in a straight line between the initial and final positions. That is, when expressing the displacement it is done in terms of the magnitude with its respective unit of measurement and the direction because the displacement is a vector type quantity. Mathematically, the displacement (Δd) is calculated as:

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<u><em>The distance it has traveled is 3,050 m and the magnitude of its displacement is 650 m north.</em></u>

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