Question

A fly enters through an open window and zooms around the room. In a Cartesian coordinate system with three axes along three edges of the room, the fly changes its position from point b (2.5 m, 2.0 m, 4.0 m) to point e (4.5 m, 3.0 m, 3.5 m). Find the scalar components of the flies displacement vector (in m).

Answer 1

The scalar components of the fly's displacement are -3.0 m in the x-direction, 3.0 m in the y-direction, and -2.0 m in the z-direction. The vector component form of the displacement is Δr = (-3.0ı, 3.0ı, -2.0ı) m, and its magnitude is approximately 4.69 m.

Step-by-step explanation:

The student asked for the scalar components of the fly's displacement vector and its magnitude when its position changes within a Cartesian coordinate system.

To calculate the scalar components of the displacement, we subtract the initial position coordinates from the final position coordinates:

Δx = xf - xo = 1.0 m - 4.0 m = -3.0 m

Δy = yf - yo = 4.5 m - 1.5 m = 3.0 m

Δz = zf - zo = 0.5 m - 2.5 m = -2.0 m

Therefore, the displacement vector in vector component form is Δr = (-3.0ı, 3.0ı, -2.0ı) m.

To find the magnitude of the displacement vector, we use the Pythagorean theorem:

| Δr | = √((-3.0 m)2 + (3.0 m)2 + (-2.0 m)2) = √(9 + 9 + 4) m = √22 m ≈ 4.69 m

Answer 2

Step-by-step explanation:

Displacement vector along x axes = 4.5 - 2.5 = 2 m

Displacement vector along y axes = 3 - 2 = 1 m

Displacement vector along z axis = 3.5- 4 = - 0.5 m

Displacement vector = 2 i + j - 0.5 k m