The magnitude of a velocity vector is called speed. Suppose that a wind is blowi
ID: 2887949 • Letter: T
Question
The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45 degrees W at a speed of 50 km/ h. (This means that the direction from which the wind blows is 45 degrees west of the northerly direction.) A pilot is steering a plane in the direction N60 degrees E at an airspeed (speed in still air) of 250 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane.
If possible please include a drawing, it would help with understanding.
Explanation / Answer
this problem requires that you find components of vectors and add them accordingly
the wind is blowing FROM the northwest, so the velocity components of the wind are:
in the + x direction with a speed of 50 cos45=35.3 km/hr
in the -y direction with a speed of 50 sin45=-35.3km/hr
for the plane, the components are:
in the +x direction 250cos30 = 216.5 km/hr
in the +y direction 250sinsin30 = 125 km/hr
the components of the plane's speed are then the sums of these components
251.8 in the +x direction
89.7 in the +y direction
magnitude = sqrt[251.8^2+89/7^2]
=267.3 km/hr
direction = arc tan[89.7/251.8]
= 19.6 degrees up from the +x axis
I hope this answer helps.
Thanks.
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