Question

What is the speed over the ground of an airplane flying at 100 km/h relative to the air caught in a 100-km/h right-angle crosswind?

Answer 1

Answer:

141.42 km/h

Explanation:

Since this is a 100km/h right angle crosswind, the speed vector with respect to the ground is the vector speed of the airplane with respect to air + the vector speed of the cross-wind with respect to the ground

<100,0> + <0,100> = <100,100>

This vector has a magnitude of

$v = \sqrt{v_1^2 + v_2^2} = \sqrt{100^2 + 100^2} = \sqrt{10000 + 10000} = \sqrt{20000} = 141.42$  km/h