Chapter 9.1, Problem 61E

True Velocity of a Jet Find the true speed and direction of the jet in Exercise 60 if the pilot heads the plane in the direction $\text{N}{\text{30}}^{\text{o}}\text{W}$.

True Velocity of a Jet A jet is flying through a wind that is blowing with a speed of $55\text{mi/h}$ in the direction $\text{N}{\text{30}}^{\text{o}}\text{W}$ (see the figure). The jet has a speed of $765\text{mi/h}$ relative to the air, and the pilot heads the jet in the direction $\text{N}{45}^{\text{o}}\text{E}$.

(a) Express the velocity of the wind as a vector in component form.

(b) Express the velocity of the jet relative to the air as a vector in component form.

(c) Find the true velocity of the jet as a vector.

(d) Find the true speed and direction of the jet.