Question

An airplane is flying in a direction of 75° north of east at a constant flight speed of 300 miles per hour.

Answer 1

The actual direction of the plane is 75° North of west with a speed of 275 mph

Explanation:

Speed of airplane = 300mph

Direction of airplane = (300 cos 75° , 300 sin 75°)

Speed of wind = 25 mph

If the wind is blowing due east then the angle is = 90° + (90 - 75)

                                                                                 = 105°

Direction of wind = (25 cos 105° , 25 sin 105°)

So,

Direction of plane + Direction of wind = Actual Direction of airplane

(300 cos 75° , 300 sin 75°) +  (25 cos 105° , 25 sin 105°) = (x, y)

( 77.65 , 289.78 ) + ( -6.47 , 24.15 ) = (x, y)

(71.18, 265.63 ) = (x, y)

Speed = $\sqrt{(71.18)^2 + (265.63)^2}$

$S = \sqrt{5066.6 + 70559.3} \\\\S = \sqrt{75625.9} \\\\S = 275 mph$

Direction:

$tan ^-^1 (theta) = \frac{265.63}{71.18} \\\\Theta = 74.99\\\\Theta = 75^o$

Therefore, the actual direction of the plane is 75° North of west with a speed of 275 mph