Question

the velocity of an airplane is 50km/hr due north. the plane the plane flies into a cross wind of 50km/hr due east at a right angle. the speed of the aircraft with respect to the ground is about

I know the answer is 70.7kn/hr,i need some work to help explain how

Answer 1

$Consider\;the\;North\;direction\;as\;the\;y-axis\;and\;the\;East\;direction\;as\;the\;x-axis\\ Then\;the\;velocity\;of\;the\;plane\;with\;respect\;to\;ground\;after\;the\;cross\;wind\;would\;be\\ v= v_{plane}+v_{wind}\\ v = 50 i\;+50j\\ (i\;being\;unit\;vector\;along\;x-axis\;and\;j\;being\;unit\;vector\;along\;y-axis) now\;the\;magnitude\;of\;the\;velocity\;would\;be\\ magnitude\;of\;velocity=speed= \sqrt{50^2+50^2}=50\sqrt2=70.7\;km/hr\\$

Answer 2

here the wind is blowing eastwards perpendicular to the direction of plane

hence the velocity of plane would be = sqrt( 50^2+ 50^2) = 70.7 kmph

Answer 3

speer with respect to ground = $\sqrt{(50)^{2}+(50)^{2}}$

                                          = $50\sqrt{2}$

                                         = 50 * 1.414

                                         = 70 . 7 km/hr