Question

You are traveling on an airplane. The velocity of the plane with respect to the air is 170.0 m/s due east. The velocity of the air with respect to the ground is 46.0 m/s at an angle of 30° west of due north.
1) What is the speed of the plane with respect to the ground?

Answer 1

Let the speed of the plane with respect to the ground is V.

The velocity of the plane with respect to the air is $V_r = 170.0 \, \text{m/s}$ due east.

The velocity of the air with respect to the ground is $V_a = 46.0 \, \text{m/s}$ at an angle of $30{}^\circ$ west of due north.

$V_x = V_r x + |V_{ax}| = 170.0 + 46.0 * \sin 30 = 170.0 + 23.0 = 193.0$

$V_y = V_r y + |V_{ay}| = 0.0 + 46.0 * \cos 30 = \text{approx. } 39.8$

$V = \sqrt{V_r x^2 + V_r y^2} = \text{approx. } 197.1$

Answer: 197.1 m/s.