Question

You are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the als and at a constant height o 7.95 × 10 m. At 1 directly above you so lhal lhe vector lead ng rom you Lll is po-7.95 x 10 m. AI I 30.0 s lhe pusilion vector leading rom you lo Lhe ar plane is p30- 8.98 x 1031+ 7.95 x 10 figure below. Determine the magnitude and orientation of the airplane's position vector at t 75.0 s. magnitude directlon 0, the airplane is as suggested in the 。above the hurizontal 90 Need Help? Read H Submit Answer Save Progress Practice Another Version

Answer 1

$\\P_{30}=P_0+V\;(t_{30}-t_0)\\\\ V=\frac{P_{30}-P_0}{t_{30}-t_0}\\\\ V=\frac{8.98\times 10^3\mathbf{i}}{30-0}=300\;\mathbf{i}\;m/s\;velocity\;of\;airplane\\\\ P_{75}=P_0+V(t_{75}-t_0)\\\\ P_{75}=7.95\times 10^3\mathbf{j}+\;300\mathbf{i}\times (75-0)\\\\ P_{75}=7.95\times 10^3\mathbf{j}+22.5\times 10^3\;\mathbf{i}\\\\ P_{75}=(22.5\times 10^3\;\mathbf{i}+7.95\times 10^3\mathbf{j} )m\\\\ magnitude\;=sqrt{(22.5\times 10^3)^2+(7.95\times 10^3)^2}=23.86\;\times 10^3\;m\\\\ direction=tan^{-1}\left ( \frac{7.95\times 10^3}{22.5\times 10^3} \right )=19.5^o$