Final answer:
The direction of the plane's displacement after 18.0 seconds, with an initial eastward velocity of 135 m/s and a northeastward acceleration of 2.18 m/s², will be approximately 16.26° north of east.
Step-by-step explanation:
To determine the direction of the displacement of the plane, we need to consider the initial velocity of the plane, the acceleration due to the wind, and the time during which the acceleration acts. The plane's initial velocity vector is entirely in the eastward direction, and the wind provides a northeastward acceleration. Over the course of 18.0 seconds, this acceleration will change the velocity of the plane in a northeastward direction, which will affect the displacement of the plane.
We can calculate the additional velocity component that the wind adds to the plane's motion in the northward direction by multiplying the acceleration by the time:
- Velocity due to wind in the northward direction = 2.18 m/s2 × 18.0 s = 39.24 m/s
Now, combining the two velocity components (the initial velocity eastward and the added velocity due to wind), we can find the overall velocity vector and consequently the displacement direction using trigonometry. The angle of the resulting displacement from the eastward direction can be found using the arctangent function:
- Angle = arctan(northward velocity/eastward velocity)
- Angle = arctan(39.24 m/s / 135 m/s)
- Angle = arctan(0.29)
- Angle ≈ 16.26° north of east
Therefore, after 18.0 seconds, the displacement of the plane will be in a direction approximately 16.26° north of east.
The complete question is given below:
A plane is flying east at 135 m/s. The wind accelerates it at 2.18 m/s² directly northeast. After 18.0 s, what is the direction of the displacement of the plane?