Airplane Velocity and Relative Motion
1) What is the speed of the plane with respect to the ground?
a) 120 m/s Submit
b) 124 m/s Submit
2) What is the heading of the plane with respect to the ground? (Let o' represent due north, 90° represents due east).
a) East of due North Submit
b) North of due East Submit
3) How far east will the plane travel in 1 hour?
Final answer:
1) What is the speed of the plane with respect to the ground?
The speed of the plane with respect to the ground is 124 m/s. This is calculated by adding the velocity of the plane (120 m/s due east) to the velocity of the air (44 m/s at an angle of 30° west of due north) using vector addition.
2) What is the heading of the plane with respect to the ground?
The heading of the plane with respect to the ground is East of due North. This direction is determined by the resultant velocity vector of the plane's motion considering both the speed and direction of the wind.
3) How far east will the plane travel in 1 hour?
The problem involves determining the resultant velocity of an airplane considering both its speed and the wind's speed and direction. The resultant velocity provides information about the plane's speed and heading with respect to the ground.
This problem requires understanding concepts of relative velocity and vector addition. Here's how we solve it:
First, calculate the resultant velocity of the plane with respect to the ground. This involves adding the velocity of the plane (120 m/s east) to the velocity of the wind (44 m/s 30° west of due north). Use trigonometry to find the resultant velocity, which gives the speed of the plane with respect to the ground.
Next, the heading of the plane with respect to the ground is determined by the resultant velocity vector. It represents the direction of the vector, calculated using inverse trigonometry functions such as arctan(y/x).
Finally, to determine how far east the plane will travel in 1 hour, multiply the eastward component of the plane's resultant velocity by the time (1 hour). This calculation provides the distance covered in the eastward direction.