Question

a man is running eastwards with 6km/h feels the wind blowing from the north, on doubling his speed he feels the wind blowing from the northeast. determine the actual direction and velocity if the wind.

Answer 1

Using +x = east and +y = north.

Suppose velocity of wind is (x,y).

Velocity of person, V = (6,0).

Velocity of wind relative to person = (x,y) - (6,0) = (x-6,y).

Since wind appears to blow directly from the north, the east-west component (x-6) must be zero.

x−6=0,

x=6 km/h.

Velocity of person, V=(4,0).

Velocity of wind relative to person = (x,y) - (12,0) = (x-12,y) = (-6,y).

Since relative velocity is from the north east (direction south west), this is an angle of atan1=45° (south of west).

The x and y components of the relative velocity must be equal, because tan45°=1.

So, y=−6 km/h.

Wind vector = (6,−6) km/h.

Wind velocity = $\sqrt{6^2+(-6)^2}$ =8.4 km/h.

Direction to the south east (from the north west).