Question

A small plane is initially flying due west with an airspeed (speed relative to the air) of 50 m/s. the plane flies into a-region where the wind is blowing toward the southwest at 20 m/s. if the pilot does not change the heading of the plane, the speed of the plane relative to the ground

a. is greater than

Answer 1

velocity of plane with respect to air is given as 50 m/s towards west

`v_(p/w) = 50 (-i)`

now speed of the wind is given as 20 m/s south west

`v_(w) = 10√(2)(-i) + 10√(2)(-j)`

now the net speed with respect to ground is given as

`v_(net) = v_w + v_(p/w)`

`v_(net) = 10\sqrt2(-i) + 10\sqrt2(-j) + 50(-i)`

`v_(net) = 64.14(-i) + 14.14(-j)`

so this speed with respect to ground is 65.7 m/s

this is greater than the speed with respect to air