Question

The pilot maintains an eastward heading while a 20 m/s wind blows northward. The plane‘s total velocity makes an angle from east

(a) sin^-1 (1/5)

(b) cos^-1 (1/5)

(c) tan^-1 (1/5)

(d) none of these

Answer 1

Correct option is (c) tan^-1 (1/5)

Because the pilot maintains an eastward heading, the engines still push the plane due east. So, v_plane ​= 100m/seastward. But the wind blows at v_wind​ = 20m/s northward, thereby knocking the plane off course by angle ϕ.

In the figure, we know the two legs but not the hypotenuse. Specifically, in units of m/s, the opposite leg has length h_o​ = 20, while the adjacent leg has length h_a​ = 100. Therefore

tanϕ = \(\frac{h_o}{h_a} = \frac{20}{100} \)

Thus ϕ = tan⁻¹\( \frac15\)