Explanation:
Let [tex]v_{a}[/tex] be the airspeed.
Let [tex]v_{w}[/tex] be the cross wind speed.
We know that,ground speed is the vector sum of airspeed and cross wind speed and airspeed is perpendicular to cross wind speed.
If [tex]v_{1}[/tex] and [tex]v_{2}[/tex] are two perpendicular vectors,the resultant vector has the magnitude [tex]\sqrt{|v|_{1}^{2}+|v|_{2}^{2}}[/tex]
Given,
[tex]v_{a}=40ms^{-1}\\v_{c}=30ms^{-1}[/tex]
So,the ground speed is [tex]\sqrt{40^{2}+30^{2}}=\sqrt{2500}=50ms^{-1}[/tex]
