Vector Application Homework: Fly from A to B in 720 km

[spoc21]

Homework Statement

A pilot wishes to fly form city A to city B, a distance of 720 km on a bearing of 070°. The speed of the plane is 700 km/h. An 60 km/h wind is blowing on a bearing of 110°. What heading should the pilot take to reach his or her destination? How long will the trip take?

Can only use the cartesian vector method for this

Homework Equations

The Attempt at a Solution

This is what I get (Please correct me if I am wrong)

We find the x and y values of the 700 vector:
=[700 cos(20°).700 sin(20°)]
=[658,239]

We now find the x and y values of the wind vector (60)
=[60 cos(20°),-700 sin(20°)]
=[56,-21]

To find the resultant, we will need to add the two vectors (correct?)

[658 + 239] + [56,-21]

Is this method correct? any help is much appreciated


Thanks!

 

[mighty2000]

Hello! Your method of using Cartesian vectors is correct. To find the resultant vector, you will need to add the x and y components of the two vectors separately. So, the resultant vector would be [658+56, 239+(-21)] = [714, 218].

To find the heading, you can use the inverse tangent function (tan^-1) to find the angle between the resultant vector and the x-axis. So, the heading would be tan^-1(218/714) = 16.7°. This means the pilot should take a heading of 070° + 16.7° = 086.7° in order to reach city B.

To find the time it takes for the trip, you can use the formula t = d/v, where t is the time, d is the distance, and v is the speed. So, t = 720/700 = 1.03 hours or approximately 62 minutes.

Hope this helps! Let me know if you have any other questions.