- #1

kaybaby

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## Homework Statement

A pilot wishes to fly form city A to city B, a distance of 720 km on a bearing of 70 degrees. The speed of the plane is 700 km/h. An 60 km/h wind is blowing on a bearing of 110 degrees. What heading should the pilot take to reach his or her destination? How long will the trip take?

## Homework Equations

Cartesian Vectors Equations

## The Attempt at a Solution

I am not sure whether i did right

First, alpha=90-70 degress=20 degrees

Let a be the direction of the 2 cities.

a=[x,y]

cos theta=cos 20=x/720

sin theta=sin 20= y/720

a=[720cos20, 720 sin 20]

a=[676.58,246.25]

Let w be the direction of wind.

110-90=20 degrees

w=[x,y]

cos y=cos20=x/60

siny = sin20=y/60

w=[56.38, =20.52]

let p be the vector of the plane

p=a+w

p=[732.96,225.73]

|p|=sqre root of 732.96^2+225/73^2

|p|= 766.93 km

time = distance/speed

=766.93km/700 km/h

=1.10 h

Since p=[732.96,224.73] we can use this info to find out the directional angle, B.

tan B=225.73/732.96

=17.12 degrees.

90-17.12 =72.88 degrees

The pilot should take the heading of 072.88 degree to reach his/her destination. It takes approx 1.10 hours.