Question

A small plane is flying horizontally due east in calm air at 250 mi/hr when it is hit by a horizontal crosswind blowing southwest at 50 mi/hr and a 30-mi/hr updraft. Find the resulting approximate speed of the plane relative to the ground to the nearest mph.

Answer 1

velocity of plane is given as

$\vec v_p = 250 \hat i$

velocity of air

$\vec v_a = -25\sqrt 2\hat i - 25\sqrt2 \hat j + 30 \hat k$

now the net speed of the plane is given as

$v = v_p + v_a$

$v  = 250 \hat i - 25\sqrt 2\hat i - 25\sqrt 2\hat j + 30 \hat k$

$v = 214.6 \hat i - 35.35\hat j+ 30\hat k$

now the net speed is

$v = \sqrt{214.6^ + 35.5^2 + 30^2}[\tex]

[tex]v = 219.55 mi/hr$

so above is the net speed of the plane