 #1
Angad401
 2
 0
 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?
 Relevant Equations:

VPE = VPA + VAG
where VPE = Velocity of the plane relative to the ground
VPA = Velocity of the plane relative to the air
VAG = Velocity of the plane relative to the ground
I was able to solve this question successfully by utilizing the sine and cosine law however my instructor said I was only allowed to utilize the vector component method, I am unsure how to complete this question using the vector component method as we have two unknowns(those being the angle of the plane's velocity relative to the air and the magnitude of the velocity of the plane relative to the ground)
My closest attempt was when I utilized variables to attempt to solve for the magnitude of VPE which would allow me to rearrange the following equation:
VPE = x[N30E]
VPA = 210[unknown angle]
VAG = 40[E]
VPE = VPA  VAG
VPA = VPE  VAG  we use this formula as we have the magnitude of VPA
This would allow me to obtain the direction she should head as well as the velocity relative to the ground
VPAx = xsin30  40
VPEy = xcos30
x = the magnitude of the velocity of the plane relative to the ground
The issue arises when I attempt to rearrange the Pythagorean equation which is as follows:
210^2 = (xsin30  40)^2(xcos3o)^2
Note: 210 ^2 = magnitude of the plane relative to the air
When I attempt to rearrange the equation I am left with a quadratic equation whose roots don't have any significance and will not provide the correct value when inputted into the prior equations
All this has led me to believe that the only way to solve these questions is to utilize the sine and cosine laws
Any help is appreciated
My closest attempt was when I utilized variables to attempt to solve for the magnitude of VPE which would allow me to rearrange the following equation:
VPE = x[N30E]
VPA = 210[unknown angle]
VAG = 40[E]
VPE = VPA  VAG
VPA = VPE  VAG  we use this formula as we have the magnitude of VPA
This would allow me to obtain the direction she should head as well as the velocity relative to the ground
VPAx = xsin30  40
VPEy = xcos30
x = the magnitude of the velocity of the plane relative to the ground
The issue arises when I attempt to rearrange the Pythagorean equation which is as follows:
210^2 = (xsin30  40)^2(xcos3o)^2
Note: 210 ^2 = magnitude of the plane relative to the air
When I attempt to rearrange the equation I am left with a quadratic equation whose roots don't have any significance and will not provide the correct value when inputted into the prior equations
All this has led me to believe that the only way to solve these questions is to utilize the sine and cosine laws
Any help is appreciated