An airplane is flying in a direction of 75 degrees north of east at a constant flight speed of 300 miles per hour. Th wind is blowing due west at a speed of 25 miles per hour. W…

Question

asked Oct 5, 2021 115k views

1 Answer

Sneal · Answer 1 · 2021-10-10T17:52:16+0000

Answer:

The resultant speed is 294.5 mi/h in a direction N79.7°E

Explanation:

Let

East and North as the positive x and y-axis, respectively.

West and South as the negative x- and y-axis, respectively.

step 1

Take the x- and y-components of the speeds.

Airplane:

$x-component = (300\ mi/hr)cos(75^o)= 77.6\ mi/h$

$y-component = (300\ mi/hr)sin(75^o)= 289.8\ mi/h$

Wind:

$x-component = -25\ mi/hr$

step 2

Adding up the components:

$x-component =77.6-25= 52.6\ mi/hr$

$y-component = 289.8\ mi/hr$

step 3

Find the resultant speed

R = √((Rx)^2 + (Ry)^2)

R = √((52,6)^2 + (289.8)^2)

$R=294.5\ mi/h$

step 4

Find the direction

$tan(\theta)=(Ry)/(Rx)$

substitute

$tan(\theta)=(289.8)/(52.6)$

$\theta=tan^(-1)((289.8)/(52.6))=79.7^o$

therefore

The resultant speed is 294.5 mi/h in a direction N79.7°E