A plane flies due north (90 degrees from east) with a velocity of 100km/h for 3 hours. During this time, a steady wind blows southeast at 30km/h at an angle of 315 degrees from due east. After 3 hours, where will the plane’s position be relative to it’s starting point? Please show all work. **Vectors and Relative Motion****Problem Description:**A plane flies due north (90° from east) with a velocity of 100 km/h for 3 hours. During this time, a steady wind blows southeast at 30 km/h at an angle of 315° from due east. After 3 hours, where will the plane's position be relative to its starting point? Show your work.**Illustration Details:**- On the left side, a diagram shows the vectors involved: - A vector labeled "plane" points straight up (north) with a magnitude of 100 km/h. - A vector labeled "wind" points downward and to the right (southeast) with a magnitude of 30 km/h. - On the right side, another diagram shows: - The vector for the plane's velocity \(v_{\text{plane}}\) represented vertically with a magnitude of 100 km/h at an angle of 90°. - The vector for the wind's velocity \(v_{\text{wind}}\) represented as a diagonal line with a magnitude of 30 km/h at an angle of 315°. - These two vectors form a right triangle.**Parameters:**- Velocity of the plane: 100 km/h at 90°.- Velocity of the wind: 30 km/h at 315°.- Time of travel: \(t = 3\) hours.**Transcription Instructions:**Please calculate where the plane will be relative to its starting point after 3 hours, considering the combined effect of plane's velocity and wind's influence. Show all steps and calculations clearly.

Name: A plane flies due north (90 degrees from east) with a velocity of 100k
Uploaded: 2024-03-20T06:57:47.000Z
Channel: Bartleby
Description: A plane flies due north (90 degrees from east) with a velocity of 100km/h for 3 hours. During this time, a steady wind blows southeast at 30km/h at an angle of 315 degrees from due east. After 3 hours, where will the plane’s position be relative to i