Question

To a man walking at 7 km/hr due west the wind appears to blow from the north-west, but when he
walks at 3 km/hr due west the wind appears to blow from the north. What is the actual direction of
the wind and what is its velocity?​

Answer 1

Answer:

Explanation:

=> To a man walking at 7 km/hr due west the wind appears to blow from the north-west:

Vm = -7 i

let Vw = x i^ + y j^

Vwm = (x + 7) i^ + y j^

tan 45° = y / x + 7

=> x + 7 = y ...(i)

=> He  walks at 3 km/hr due west the wind appears to blow from the north:

Vm = -3 i^

Vwm = (x + 3) i^ + y j^

Thus, x + 3 = 0

x = -3 ... (ii)

=> Solving (i) and (ii), we get

y = -3+7 = 4

∴ Vw = -3 i^ + 4 j^

θ = tan⁻¹ (4/-3) = -53°

here,  θ = -53° which means it blows 53° from west

V = √(-3)² + (4)²

= 5 km /h

=> Thus, the actual direction of  the wind is west and its velocity is 5km/h.