The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by and . The magnitude, in meters, of the plane's displacement from the origin is A) 9.14 × 10³. B) 1.61 × 10⁴. C) 1.84 × 10⁴. D) 9.14 × 10³t. E) 1.61 × 10⁴t.

Question

Quizplus · Accepted Answer

The displacement vector is given by the difference between the final and initial positions:
d = (21400-500, 9000-2500, 1200-100) = (20900, 6500, 1100)
The magnitude of the displacement vector is given by the formula ||d|| = sqrt(x^2 + y^2 + z^2), where x, y, and z are the components of the displacement vector. Substituting the values, we get:
||d|| = sqrt(20900^2 + 6500^2 + 1100^2) ≈ 1.84 × 10^4
Therefore, the best choice is C.

The Site from Which an Airplane Takes Off Is the Origin