When an airplane flies, its total velocity with respect to the ground is:

v total = v plane + v wind

where v plane denotes the plane's velocity through motionless air, and v wind denotes the wind's velocity. Crucially, all the quantities in this equation are vectors. The magnitude of a velocity vector is often called the "speed". Consider an airplane whose speed through motionless air is 100 m/s. To reach its destination, the plane must fly east. The "heading" of a plane is the direction in which the nose of the plane points. So, it is the direction in which the engines propel the plane.

(i) If the plane has an eastward heading, and a 20 m/s wind blows towards the southwest, then the plane's speed is–