Solve Vector Plane Problem: Airplane to Lake 250 km Away

[Trooper100]

Homework Statement

****If anyone could help me, it would be much appreciated. I have attempted several times, but my answers aren't correct. I want to see what everyone else got.

If possible, a diagram would be great. Thank you very much everyone.

a pilot wants to fly her plane to a lake that is 250 km [N 30.0 E] from her starting point. The plane has an air speed of 210 km/h, and a wind is blowing from the west at 40.0km/h.

a) in what direction should she head the plane to fly directly to the lake?

b) if she uses the heading determined in a, what will be her velocity relative to the ground?

c) how long will it take her to reach her destination.

Homework Equations

Cosine and sine laws.

Basic equations

V = displacement / time

a = change in velocity / time

Answers

a) N20.5E

b) 227km/h [N30.0E]

c) 1.10h

These answers may be wrong. My textbook does that a lot. :(

This is a simple intro-physics vector problem. It has no relationship to space, time, black holes, nuclear bombs or any advanced physics. Thank you.

 

[Filip Larsen]

It may help to draw a so-called wind triangle with the sides representing the planes air speed vector, the wind vector and their combination into the planes ground speed vector. You can then either use vector calculations to calculate the answers or use pure trigonometry.