Velocity Question?

Question

A novice polot sets a plane's controls, thinking the plane will fly at 250 km/h to the north. If the wind blows at 75 km/h toward the southeast, what is the plane's resultant velocity?

Answer 1

Do it graphically.
Draw a line vertically, length scaled to 250.
The wind is blowing against him and therefore will slow him down
If you draw 4 quadrants the 250 will be the vert line.
from the end of the vertical line at the top draw a vector S.E.(i.e. 45*) at a length of 75.(in the first quadrant)
Measure the length from the centre to the end of the 75 line. This will give you the plane's final speed and direction

Answer 2

i assume you mean the wind is a nor-westerly

the plane would fly north!

if the pilot set the controls then it must be assumed that :
1 he is maualy flying the plane on instruments and will stay on course at the same speed
2 he set the autopilot which would compensate for anychanges in diection and speed

if he had an old enough plane so that the computer would not do corrections then he would not be able to 'set' the controls

hope i answered your question as fully as you need

useing the correct terminaology would make it extremely difficult for the average person to understand

Answer 3

OK look you didn't give OT enough info eg: the time it takes to get to where he's flying. i would suggest you do it this way - draw the vector diagram according to scale. fill in all the info given!! if i have all this correct, your vector diagram should be a 90 degree triangle with the wind being your hypotenuse - therefor you can use Pythagoras to work out the resultants velocity. man does this make sense? does this help

Answer 4

the resultant velocity = velocity of plane +velocity of wind
from the quetion .resolve the direction for the velocity of plane and wind

velocity of plane = 250 (diretion north)
250 j

velocity os wind= 75 (direction southeast)
southeast means with 45angel to axis
{ ( 75sin45 )i - (75cos45)j}
so.now add the two velocity with their direction

resultant velocity=
= 250 j +[(75sin45)i -(75cos45)j]=

53.03 i +197 j
and the magnitude of this velocity =
sqr root ((53.03)^2+(197)^2) = 204km/h

Answer 5

The question is unanswerable if you donot tell us the distance. For an observer on earth would also need to consider the direction of earth's rotation (Thus add another vector to the wind's direction)

Answer 6

the two velocities are 250 kmphdue north and 75 kmph due south
resolving the elocity of the wind inthe south and east direction
due south=75rt2/2 and due east=75rt2/2
resultant=[(250-75rt2/2)^2+(75rt2/2)^2]^1/2
=[62500+5625+5625-26520.51]^1/2
=218.3kmph
direction=tan theta=[75rt2/2/(250-75rt2/2]

Answer 7

velocity is speed, it is not determined by either wind or direction