Question

Consider flying between Los Angeles and San Francisco, as shown in the image below. Assume that San Francisco is directly north of Los Angeles, and that the two cities are separated by a distance D=377D=377 miles. The engines of the plane (as with any plane) maintain its speed relative to the air, which for the sake of this problem we take to be constant. Denoting the velocity of the plane relative to the air by v⃗p/a​v​⃗​​​p/a​​, this means that ∣v⃗p/a∣=v0=424∣​v​⃗​​​p/a​​∣=v​0​​=424 mph where v0>0v​0​​>0 is constant. The air can also be moving with respect to the ground (a phenomenon that we call wind) with a velocity vector that we'll denote by v⃗a/g,​v​⃗​​​a/g​​, thus making the plane's velocity vector relative to the ground, v⃗p/g​v​⃗​​​p/g​​, given by

v⃗p/g=v⃗p/a+v⃗a/g​v​⃗​​​p/g​​=​v​⃗​​​p/a​​+​v​⃗​​​a/g​​

Suppose that wind is blowing due East (recall that LA is directly south of SF) with constant speed ∣v⃗a/g∣=w0=47.1∣​v​⃗​​​a/g​​∣=w​0​​=47.1 mph, how long does it take make a roundtrip from LA to SF and back?

Answer 1