Question

A jet airplane is traveling west from Austin, Texas to Miami, Florida. It has an average speed with no wind of 600 mph. An observer on the ground records the airplane of having a speed of 580 mph. What speed and direction is the wind moving?

Answer 1

consider the west direction as positive direction of motion

V' = velocity of airplane relative to observer on ground = 580 mph

v = velocity of wind relative to observer on ground

V = average speed of airplane with no wind = 600 mph

relative velocity is given as

V' = V + v

inserting the values

580 = 600 + v

v = 580 - 600

v = - 20 mph

the negative sign indicates the direction of wind is opposite to direction of airplane , east

hence speed of wind is 20 mph in east direction.

Answer 2

Velocity of airplane without any wind

$v_1 = 600 mph$

now when air is blowing with some speed then the net speed is observed by the observer

$v_{net} = 580 mph$

now we will have

$v_{net} = v_1 - v_w$

wind speed here is given as $v_w$

now here we will have

$580 = 600 - v_w$

$v_w = 20 mph$

so wind speed will have 20 mph