Answer to Question #72956 in Classical Mechanics for Blaney

Question

An airplane is flying from San Francisco to Seattle which is a distance of approximately 1200 km. The cruising speed of the plane (VP) is 400 km/hr relative to the air, and on a calm day (no wind) the pilot would fly on a path, due north, arriving in Seattle exactly 3.0 hours after leaving San Francisco(ignoring the time spent taxiing, taking off, landing etc.). However, today, the wind is blowing due east with a constant velocity (VW) of 50 km/hr relative to the ground, and the pilot has not taken this into account. Without paying attention, the pilot keeps the plane pointed due north for the entire flight.

1.) (3 points) Relative to the ground, in which direction is the plane flying (use theta for angles: θ)? Derive an algebraic solution and then give a numerical answer (three significant figures is fine) expressed in degrees relative to due north (e.g. ’45.0° west of north’).

Answer 1

v_p=v cos⁡θ
v_w=v sin⁡θ
v_w/v_p =(v sin⁡θ)/(v cos⁡θ )=tan⁡θ
θ=tan^(-1)⁡〖v_w/v_p 〗
θ=tan^(-1)⁡〖50/400〗=7.125°