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Question
(a) Another airplane is flying in a jet stream that is blowing at 45.0 m/s in a direction $20^\circ$ south of east (as in Exercise 3.58). Its direction of motion relative to the Earth is $45.0^\circ$ south of west, while its direction of travel relative to the air is $5.00^\circ$ south of west. What is the airplane's speed relative to the air mass? (b) What is the airplane's speed relative to the Earth?
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Final Answer
  1. $63.4 \textrm{ m/s}$
  2. $29.6 \textrm{ m/s}$

Note: at about 6:20, Shaun says "the velocity of the air with respect to the ground", but he meant to say "the velocity of the airplane with respect to the ground". Obviously, this correction also applies when he said "the velocity of the air with respect to the wind", which should be "the velocity of the airplane with respect to the wind" since you can't have the velocity of something (air) with respect to itself (wind) besides the trivial answer of zero.

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OpenStax College Physics Solution, Chapter 3, Problem 60 (Problems & Exercises) (12:33)

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