Why Is My Calculation for the Plane's Correct Heading Incorrect?

[turpy]

Homework Statement
A plane has an airspeed of 200 mph. The pilot wishes to reach a destination 600 mi due east, but a wind is blowing at 10.0 mph in the direction 10.0 degrees north of east.
In what direction must the pilot head the plane in order to reach her destination?


______________ degrees south of east

The attempt at a solution
I drew two vectors
one horizontal facing east of magnitude 200 mph (plane) + 10cos10 (wind)
and one vertical of magnitude 10sin10
I solved for the angle b/w the horizontal vector and the resultant vector
arctan theta = (10sin10/(200+10cos10))
and I get that theta = 0.474 degrees south of east

When I type this answer (0.474) into masteringphysics.com, it tells me that I'm incorrect.
What is it that I'm doing wrong?

Thanks!

 

[AC130Nav]

Homework Statement
A plane has an airspeed of 200 mph. The pilot wishes to reach a destination 600 mi due east, but a wind is blowing at 10.0 mph in the direction 10.0 degrees north of east.
In what direction must the pilot head the plane in order to reach her destination?


______________ degrees south of east

The attempt at a solution
I drew two vectors
one horizontal facing east of magnitude 200 mph (plane) + 10cos10 (wind)
and one vertical of magnitude 10sin10
I solved for the angle b/w the horizontal vector and the resultant vector
arctan theta = (10sin10/(200+10cos10))
and I get that theta = 0.474 degrees south of east

When I type this answer (0.474) into masteringphysics.com, it tells me that I'm incorrect.
What is it that I'm doing wrong?

Thanks!

Your wind triangle is in error. The desired ground track (velocity unknown) is due east; the 200 mph is the length of a vector along the new heading which you have yet to determine.

I really have no idea how your formula means.

 

[turpy]

OH! thank you so much i get it now

now i have arcsin theta = (10sin10)/200
theta = 0.497 south of east, which is the correct answer

a simple question but i totally misinterpreted what "airspeed" meant

 

[AC130Nav]

You're welcome.

As a navigator if I fed that to the pilot he'd try to do it, but share a laugh with the copilot. But that's when there were navigators.

 

[rwisz]

I would suggest double-checking your calculations and making sure you are using the correct units for each value (mph for speed, degrees for angles). Additionally, it is important to consider the direction of the wind in relation to the plane's heading. In this problem, the wind is blowing in a direction 10 degrees north of east, so the plane's heading must be in a direction south of east in order to counteract the wind and reach the destination. I would recommend drawing a diagram to visualize the problem and make sure all calculations and directions are accurate.