Answer:
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 = [tex]\sqrt{374.70^2+40.56^2} = 376.89 mi/hr[/tex]
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.
