Word problem: A plane is headed N 40° E with a speed of 600

[Faded-Maximus]

Word problem: A plane is headed N 40° E with a speed of 600

A plane is headed N 40° E with a speed of 600 km/h. A west wind causes it to travel N 45° E. Find the resultant speed of the plane and the speed of the wind.

I am having difficulties starting this question, if somebody could give me some help and leader me in the right direct that would be great.

Thanks

 

[skeeter]

let V = resultant groundspeed of the plane
W = wind speed


in the x-direction ...

600cos(50) + W = Vcos(45)


in the y-direction ...

600sin(50) + 0 = Vsin(45)


you have two equations with two unknown values (W and V) ... solve the system.

 

[Faded-Maximus]

Thanks for your help although I guess I should have been more specific on how to do it since there are numerous solutions. Here is an example of something similar we have completed in class.

A small aircraft is flying on a heading of 330° at a constant speed of 150 km/h. The wind is blowing on a bearing of 085° with a speed of 40 km/h. Determine the actualy speed and direction of the aircraft relative to the ground.

Solution:

OR is the resulant vector.
<WOH = 115° so <OHR = 65°
use cosine law
r^2 = 40^2 + 150^2 - 2(40)(150)cos65
r = 137.9

now use sine law to find <ROH
sinx / 40 = sin65 / 138
x = 15

Therefore, the bearing = 330 + 15
= 345

The plane is flying on a vearing of 345° at a speed of 138km/h.

If somebody could help me set it up similar to this, that would be great. Thanks again.

 

[skeeter]

suit yourself ... you have a sketch of the vector sum?

using the law of sines,
W/sin(5) = 600/sin(45)

once you get W ...

W/sin(5) = V/sin(130)

 

[Faded-Maximus]

Thanks alot