How Should a Pilot Adjust Her Course in Wind to Reach a Target?

[FlipMC]

Relative Velocities & Vectors [MULTIPLYING/DIVIDING VECTORS]

Homework Statement

A bush pilot wants to fly her plane to a lake that is 250.0 km [N30°E] from her starting point. The plane has an air speed of 210. km/h, and a wind blowing from the west at 40.0 km/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?

Homework Equations

c^2 = a^2 + b^2

The Attempt at a Solution

http://img340.imageshack.us/img340/1715/phy1.jpg

(a) sin0 = 40/210
0 = sin-1(0.19)
0 = 10.95°
0 = Degree

30° - 10° = [N20°E]

(b) Va^2 = Val^2 + Vwa^2
= 210^2 + 40^2
= 44,100 + 1600

Va = √45, 700
Va = 213.7m/s

4. The answers from the textbook

(a) N20.5°E

(b) 227 km/h [N30.0°E]

So how come I am getting different answers? :s

 

[willem2]

(a) sin0 = 40/210
0 = sin-1(0.19)
0 = 10.95°
0 = Degree

30° - 10° = [N20°E]

I have no idea what you're trying to do here. Suppose the airspeed makes an angle
A east of north. What are the north/south and east/west components of the airspeed?
And what are the components of the ground speed?
what is the angle the ground speed makes with north, if you know the n/s and e/w components?

(b) Va^2 = Val^2 + Vwa^2

you can only use pythagoras if the Val and Vwa are at right angles.

 

[kuruman]

To begin with, your drawing shows the wind blowing from the East, assuming that North is straight up. You need to reverse its direction.

Secondly, 210 km/h is the speed of the plane relative to the air not the lake.

You need to treat this as a relative velocity problem in two dimensions where you have to keep the vertical and horizontal components separate from each other. Let

v_PL = velocity of plane relative to the lake (what you are looking for)
v_AL=velocity of plane relative to the lake
v_PA=velocity of plane relative to the air

Then v_PL=v_AL+v_PA

Remember that this is vector addition.