Vector story problem

medicalphysicsguy

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Jan 23, 2012
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An airplane is flying in the direction 150 degrees with an airspeed of 300 mph, and the wind is blowing at 30mph in the direction 60 degrees. Approximate the true course and the ground speed of the airplane.

I get:

Plane:

u1=300cos(π/6)=300.866=260\displaystyle u_{1}=300*cos( \pi /6) = 300*.866 = 260
u2=300sin(π/6)=30012=150\displaystyle u_{2}=300*sin( \pi /6) =300*\frac{1}{2} = 150

Wind:

v1=30cos(π/3)=3012=15\displaystyle v_{1}=30*cos ( \pi /3) = 30*\frac{1}{2} = 15
v2=30sin(π/3)=30.866=26\displaystyle v_{2}=30*sin( \pi /3) = 30*.866 = 26

Results:

u1v1=245\displaystyle u_{1}-v_{1} = 245
u2v2=124\displaystyle u_{2}-v_{2} = 124
Speed=2452+1242=274.6\displaystyle Speed = \sqrt{245^2 + 124^2} = 274.6

Angle = .55 rads 148.8 degrees

Book says: 301.5 mph, 144.3 degrees

What is my dumb mistake? I cannot figure it out.

Thanks
mpg
 
Last edited:
An airplane is flying in the direction 150 degrees with an airspeed of 300 mph, and the wind is blowing at 30mph in the direction 60 degrees. Approximate the true course and the ground speed of the airplane.

I get:

Plane:

u1=300cos(π/6)=300.866=260\displaystyle u_{1}=300*cos( \pi /6) = 300*.866 = 260 <<<< U1 = 300 * cos(5π/6) = -259.808



u2=300sin(π/6)=30012=150\displaystyle u_{2}=300*sin( \pi /6) =300*\frac{1}{2} = 150

Wind:

v1=30cos(π/3)=3012=15\displaystyle v_{1}=30*cos ( \pi /3) = 30*\frac{1}{2} = 15
v2=30sin(π/3)=30.866=26\displaystyle v_{2}=30*sin( \pi /3) = 30*.866 = 26

Results:

u1+v1=245\displaystyle u_{1} + v_{1} = -245
u2+v2=176\displaystyle u_{2} + v_{2} = 176
Speed=u2+v2=274.6\displaystyle Speed = \sqrt{u^2 + v^2} = 274.6

Angle = .55 rads 31.8 degrees

Book says: 301.5 mph, 144.3 degrees

What is my dumb mistake? I cannot figure it out.

Thanks
mpg

.
 
Last edited by a moderator:
An airplane is flying in the direction 150 degrees with an airspeed of 300 mph, and the wind is blowing at 30mph in the direction 60 degrees. Approximate the true course and the ground speed of the airplane.

I get:

Plane:

u1=300cos(π/6)=300.866=260\displaystyle u_{1}=300*cos( \pi /6) = 300*.866 = 260
u2=300sin(π/6)=30012=150\displaystyle u_{2}=300*sin( \pi /6) =300*\frac{1}{2} = 150

Wind:

v1=30cos(π/3)=3012=15\displaystyle v_{1}=30*cos ( \pi /3) = 30*\frac{1}{2} = 15
v2=30sin(π/3)=30.866=26\displaystyle v_{2}=30*sin( \pi /3) = 30*.866 = 26

Results:

u1v1=245\displaystyle u_{1}-v_{1} = 245
u2v2=124\displaystyle u_{2}-v_{2} = 124
Speed=2452+1242=274.6\displaystyle Speed = \sqrt{245^2 + 124^2} = 274.6

Angle = .55 rads 148.8 degrees

Book says: 301.5 mph, 144.3 degrees

What is my dumb mistake? I cannot figure it out.

Thanks
mpg


Airplane = <300cos(150),300sin(150)>\displaystyle \displaystyle <300\cos(150^\circ),300\sin(150^\circ)> = <259.81,150>\displaystyle \displaystyle <-259.81,150>

Wind = <30cos(60),30sin(60)>\displaystyle \displaystyle <30\cos(60^\circ),30\sin(60^\circ)> = <15,25.98>\displaystyle \displaystyle <15,25.98>

Airplane + Wind = <244.81,175.98>\displaystyle \displaystyle <-244.81,175.98>

Ground Speed = (244.81)2+(175.98)2=301.5\displaystyle \displaystyle \sqrt{(-244.81)^2+(175.98)^2}=301.5 mph

Direction = arctan(175.98244.81)+180=144.3\displaystyle \displaystyle \arctan(\frac{175.98}{-244.81})+180^\circ=144.3^\circ
 
Last edited:
Oh I see it, I subtracted in both cases, but y component is additive. Should have been more careful with my positives and negatives. Thanks!
 
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