A duck waddles 2.3m east and 7.0m north. what are the magnitude and direction of the ducks displacement with respect to its original position?
new displacement=2.3E+7N
magnatude=sqrt (2.3^2 + 7^2)
direction arctan 2.3/7 E of N
To find the displacement of the duck, we can use the Pythagorean theorem to calculate the magnitude and trigonometry to calculate the direction.
Step 1: Calculate the magnitude (or the length) of the displacement.
Using the Pythagorean theorem, we can find the magnitude of the displacement by squaring the length traveled in the east-west direction and adding it to the square of the length traveled in the north-south direction, and then taking the square root of the result.
Magnitude = √(2.3^2 + 7.0^2) ≈ √(5.29 + 49) ≈ √54.29 ≈ 7.37 meters.
Step 2: Calculate the direction of the displacement.
To find the direction, we can use trigonometric functions such as sine and cosine. The direction angle (θ) is determined by taking the inverse tangent of the ratio of the northward displacement to the eastward displacement.
θ = arctan(7.0 / 2.3) ≈ 73.5 degrees (rounded to one decimal place).
Therefore, the magnitude of the duck's displacement is approximately 7.37 meters, and it is at an angle of approximately 73.5 degrees north of east.
To find the magnitude and direction of the duck's displacement, we can use the Pythagorean theorem and trigonometry.
First, let's calculate the magnitude of the displacement. According to the Pythagorean theorem, the magnitude (d) of the displacement is given by the equation:
d = √(Δx² + Δy²)
Where Δx is the change in the eastward direction (2.3m) and Δy is the change in the northward direction (7.0m).
Substituting the values, we have:
d = √(2.3² + 7.0²)
= √(5.29 + 49)
= √54.29
≈ 7.37m
So, the magnitude of the duck's displacement is approximately 7.37m.
Now, let's find the direction of the displacement. We can use the tangent function (tanθ) to find the angle (θ) between the displacement vector and the eastward direction.
θ = atan(Δy / Δx)
Substituting the values, we have:
θ = atan(7.0 / 2.3)
≈ 73.4°
Therefore, the direction of the duck's displacement with respect to its original position is approximately 73.4° north of east.