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

$v_{w} = 10\sqrt{2}(-i) + 10\sqrt{2}(-j)$

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