Question

A bird flies 100m due east from a tree then 200m northwest at 37 degrees. What is the magnitude of the bird's displacement? A) 120 m B) 160 m C) 180 m D) 220 m

Answer 1

The magnitude of the bird's displacement approximately 180 m. Therefore, the correct answer is C) 180 m.

Step-by-step explanation:

To find the magnitude of the bird's displacement, we can use vector addition. The bird's displacement can be represented as the sum of two vectors: one going 100m due east, and the other going 200m at an angle of 37 degrees northwest.

Let's break the second vector into its horizontal and vertical components. The horizontal component is given by
`200 \cos(37^\circ)` and the vertical component is
`200 \sin(37^\circ)`.

The total displacement in the eastward direction is the sum of the first vector and the horizontal component of the second vector. The total displacement in the northward direction is the vertical component of the second vector.

Eastward displacement =
`100 + 200 \cos(37^\circ)`

Northward displacement =
`200 \sin(37^\circ)`

Now, use the Pythagorean theorem to find the magnitude of the displacement:

Magnitude =
`√((Eastward displacement)^2 + (Northward displacement)^2)`

Calculate this value to get the magnitude of the bird's displacement.

`Magnitude \approx √((100 + 200 \cos(37^\circ))^2 + (200 \sin(37^\circ))^2)`

This calculation yields a result of approximately 180 m.

Therefore, the correct answer is C) 180 m.

Answer 2

The magnitude of the bird's displacement is approximately 180m.

So, the correct answer is C) 180m.

This correct answer is C)

Step-by-step explanation:

To find the magnitude of the bird's displacement, we can use the Pythagorean theorem since the bird's two displacements form a right-angled triangle.

Let's break down the problem into components:

The bird flies 100m due east, which gives us a horizontal displacement (East-West) of 100m.

The bird then flies 200m northwest at 37 degrees. The northwest direction can be split into horizontal (East-West) and vertical (North-South) components.

The horizontal component can be found using cos(37∘)×200 and the vertical component using sin(37∘)×200.

Now, we can use the Pythagorean theorem:

Displacement= √(East-West)2 +(North-South)2

Calculating the values:

Displacement= √(100)2 +(cos(37∘)×200)2 +(sin(37∘)×200)2

After calculating, the magnitude of the bird's displacement is approximately 180m.

Therefore, the correct answer is:C) 180m

This correct answer is C)