Answer:
The resultant speed is 294.5 mi/h in a direction N79.7°E
Step-by-step 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:
[tex]x-component = (300\ mi/hr)cos(75^o)= 77.6\ mi/h[/tex]
[tex]y-component = (300\ mi/hr)sin(75^o)= 289.8\ mi/h[/tex]
Wind:
[tex]x-component = -25\ mi/hr[/tex]
step 2
Adding up the components:
[tex]x-component =77.6-25= 52.6\ mi/hr[/tex]
[tex]y-component = 289.8\ mi/hr[/tex]
step 3
Find the resultant speed
[tex]R = \sqrt{(Rx)^2 + (Ry)^2}[/tex]
[tex]R = \sqrt{(52,6)^2 + (289.8)^2}[/tex]
[tex]R=294.5\ mi/h[/tex]
step 4
Find the direction
[tex]tan(\theta)=\frac{Ry}{Rx}[/tex]
substitute
[tex]tan(\theta)=\frac{289.8}{52.6}[/tex]
[tex]\theta=tan^{-1}(\frac{289.8}{52.6})=79.7^o[/tex]
therefore
The resultant speed is 294.5 mi/h in a direction N79.7°E
