Serway & Jewett — Vectors: Problem 31

Review. You are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the x axis and at a fixed height of \(7.60 \times 10^3\) m. At time \(t = 0\), the airplane is directly above you so that the vector leading from you to it is \(\vec{P}_0 = 7.60 \times 10^3 \hat{j}\) m. At \(t = 30.0\) s, the position vector leading from you to the airplane is \(\vec{P}_{30} = (8.04 \times 10^3 \hat{i} + 7.60 \times 10^3 \hat{j})\) m as suggested in Figure P3.31. Determine the magnitude and orientation of the airplane's position vector at \(t = 45.0\) s.