Velocity question...?

Question

A light plane is travelling at 175 km/h on a heading of N8˚ E in a 40 km/h wind from N80˚ E. Determine the plane's ground velocity?

Answer 1

Trigonometry time.

Draw a triangle representing motion of the plane.  Sin8*175 gives you a vertical velocity of 24.4 km/h [North].  Cos 8*175 gives you a horizontal velocity of 173.3 km/h [East].

Second triangle for motion of wind.  It comes from NE, so draw it going SW.  Sin80*40 gives vertical velocity of 39.4 km/h [South].  Cos 80*40 gives horizontal velocity of 6.95 km/h [West].

Add the horizontal and vertical vectors and draw a new triangle with the totals.

Horizontal:  173.3 km/h [East] - 6.95 m/s [West] = 166.35 km/h [East].

Vertical:  24.4 km/h [North] - 39.4 km/h [South] = 15 km/h [South]

With this new triangle you take the tan (opposite/adjacent) to get the angle 5.15° South of East.

Solving for the hypotenuse will give you a velocity of 167 km/h.

So the plane's ground velocity (or apparent velocity for an observer on the ground) is 167 km/h at 5.15° South of East.