Apilot heads his jet due east. the jet has a speed of 425 mi/h relative to the air. the wind is blowing due north with a speed of 35 mi/h. (assume that the i vector points east, and the j vector points north.)
(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.

(a)Velocity of wind = 35 j

(b)Velocity of jet relative to air = 425 i

(c)True velocity of jet = 425 i + 35 j

(d)True speed of jet = = 426.88 mi/h

    Direction of jet is, ∅ = = 5.38°

Explanation:

We can represent east direction by i and north direction by j.

The jet has a relative speed of 425 mi/h relative to the air.

The wind is blowing due north with a speed of 35 mi/h = 35 j

425 mi/h is the relative speed with respect to wind that is

Velocity of jet wrt wind= =

                               425 i = - 35 j

= 425 i + 35 j

(a)Velocity of wind = 35 j

(b)Velocity of jet relative to air = 425 i

(c)True velocity of jet = 425 i + 35 j

(d)True speed of jet = = 426.88 mi/h

    Direction of jet is,

     ∅ = = 5.38°

resonant frequency

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm