Vectors Applications: Solving Pilot Trip from City A to City B

[kaybaby]

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.

 

[mighty2000]

Your solution looks correct, but I would suggest using the Pythagorean theorem to find the magnitude of p instead of calculating the square root of the components separately. Also, I would recommend rounding your answer for the heading to the nearest degree. Additionally, it might be helpful to draw a diagram to visualize the problem and your solution. Overall, good job on solving the problem!