Please answer the following question. Thank you! A small plane must fly from loc
ID: 1652009 • Letter: P
Question
Please answer the following question. Thank you!
A small plane must fly from location A to location B in 2 hours. B is 200 miles away from A and is in the direction 20 degree south of east. At the plane's altitude there is a 25 mph wind that is blowing 30 degree north of east, what is the minimum average speed relative to the air the plane must maintain to make the trip? What direction must the plane fly relative to the air? Use the formalism from class, assume a straight line path, and include a labeled vector sketch. You must clearly define two different reference frames for full credit.Explanation / Answer
in the reference frame of earth.
r = 200 (cos20i - sin20j) = 188i - 68.4j miles
v_air = 25(cos30i + sin30j) = 21.6i + 12.5j mph
v_plane = r / t = (188i - 68.4j) / 2
v_plane = 94i - 34.2j mph
this is the velocity of plane as observed from earth.
and we observe from the reference frame of air.
then v_plane_air = v_plane - v_air
v = ( 94i - 34.2j) - (21.6i + 12.5j)
v = 72.4i - 46.7j mph
average speed = magnitude = sqrt(72.4^2 + 46.7^2)
= 86.2 mph ........Ans
direction =tan^-1(46.7 / 72.4) = 33 deg south of east.
.........Ans