Vector story problem

[medicalphysicsguy]

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:

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

Wind:

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

Results:

\(\displaystyle u_{1}-v_{1} = 245\)
\(\displaystyle u_{2}-v_{2} = 124\)
\(\displaystyle Speed = \sqrt{245^2 + 124^2} = 274.6\)

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

 

[Deleted member 4993]

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:

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

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

Wind:

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

Results:

\(\displaystyle u_{1} + v_{1} = -245\)
\(\displaystyle u_{2} + v_{2} = 176\)
\(\displaystyle Speed = \sqrt{u^2 + v^2} = 274.6\)

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

.

 

[srmichael]

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:

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

Wind:

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

Results:

\(\displaystyle u_{1}-v_{1} = 245\)
\(\displaystyle u_{2}-v_{2} = 124\)
\(\displaystyle Speed = \sqrt{245^2 + 124^2} = 274.6\)

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

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

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

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

Direction = \(\displaystyle \displaystyle \arctan(\frac{175.98}{-244.81})+180^\circ=144.3^\circ\)

 

[medicalphysicsguy]

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!