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To a man walking North at 4m/s, a constant wind appears to have a speed f 3m/s. The man then changes direction, and when he is walking West at 3m/s the wind appears to have a speed of 4 m/s. There are two possible wind velocities.

If I and j are unit vectors in the east and north directions, respectively:

1) Show that -3i + 4j is one possible wind velocity

2) Find the second possible wind velocity.

Ok, so this is what I¡¦ve got so far:

Vm (Velocity of man) = 4m/s = 4j m/s. (When wind appears to have Vw (Velocity of wind) of 3m/s)

Vm (Velocity of man) =3m/s = 3i m/s (wind appears to have Vw (Velocity of wind) of 4m/s)

Vm = 4j

Vwm = xi

Vw = ai + bj

Vwm = Vw ¡V Vm

Xi = ai + bj ¡V 4j

Xi = ai + bj +0i -4j

„Ã xi = ai

„Ã x = a

„Ã 0 = b ¡V 4

„Ã b=4

Vm = -3i

Vwm = yi ¡V yj

Vw = ai + bj

Vwm = Vw ¡V Vm

Yi ¡V yj = (ai + bj) + 3i

„Ã yi = ai +3i

„Ã -y = b

„Ã y = -4

Y = a ¡V 3

-4 = a ¡V 3

1 = a

This gives me a velocity of 1i + 4j.

Have i gone totally wrong, or have i just found the answer to part two instead of part one?

If so, what do i do next to find the second velocity, or, if its all just totally wrong, how should i actually go about doing the question?

Thanks in advance for any help you can give.