Ajet airliner moving initially at 300 mi/h due east enters a region where the wind is blowing at 85 mi/h in a direction 28.5° north of east. what is the new velocity of the aircraft relative to the ground?

   Velocity of aircraft relative to the ground = 376.89 mi/hr in a direction 6.18⁰north of east.

Explanation:

   Let east represents positive x- axis and north represent positive y - axis. Horizontal component is i and vertical component is j.

  A jet airliner moving initially at 300 mi/h due east, Velocity = 300 i mi/hr

   Wind is blowing at 85 mi/h in a direction 28.5° north of east, which means wind is blowing at 85 mi/h in a direction 28.5° to positive X- axis.

    Velocity of wind = 85 cos 28.5 i + 85 sin 28.5 j = (74.70 i + 40.56 j) mi/hr

    So velocity of aircraft relative to the ground = 3001 i + (74.70 i + 40.56 j)

                                                                              = (374.70 i + 40.56 j) mi/hr

     Magnitude of velocity =

     Direction, θ to positive X -axis = tan⁻¹(40.56/374.70) = 6.18⁰ = 6.18⁰north of east.

     So velocity of aircraft relative to the ground = 376.89 mi/hr in a direction 6.18⁰north of east.