The Physics of Airplane Velocity

1) What is the speed of the plane with respect to the ground?
2) What is the heading of the plane with respect to the ground?
3) How far east will the plane travel in 1 hour?

1. The speed of the plane with respect to the ground is 95.39 m/s.
2. The heading of the plane with respect to the ground is 20.93° east of due north.
3. In one hour, the plane will travel 324 km eastward.

To solve the problem, we need to understand the vectors involved in the motion of the airplane. The velocity of the plane with respect to the air is given as 110.0 m/s due east, and the velocity of the air with respect to the ground is 40.0 m/s at an angle of 30° west of due north.

1) The speed of the plane with respect to the ground is determined by adding the velocities of the plane and the air using vector addition. By decomposing the air's velocity into northward and westward components, we find that the eastward velocity of the plane relative to the ground is 90.0 m/s. Using the Pythagorean theorem, we calculate the speed of the plane with respect to the ground to be 95.39 m/s.

2) The heading of the plane with respect to the ground is found by calculating the inverse tangent of the ratio of the northward component to the eastward component. This gives us a heading of 20.93° east of due north.

3) In one hour, the plane will travel eastward a distance equal to the eastward component of the ground velocity multiplied by the time. This results in the plane traveling 324 km eastward in one hour.