Question

A steamer is moving due east with 36 km/h. To a man in the steamer the wind appears to blow at 18 km/h due north. Find the velocity of the wind.

• A. 5√5 ms^-1 30^o North of east
• B. 5 ms^-1 60^o North of east
• C. 5√5 ms^-1 60^o North of east
• D. 5 ms^-1 30^oNorth of east

Answer 1

Answer: (A)

5√5 ms^-1 30^o North of east

Answer 2

V_ws= V_w- V_s ⇒ (V_wx$\widehat{i}$ + V_wy$\widehat{j}$) - 10$\widehat{i}$ = 5$\widehat{j}$ or (V_wx$\widehat{i}$ + V_wy$\widehat{j}$) = 5$\widehat{j}$ + 10$\widehat{i}$

|V_w| = 5√5 tan θ = 1/2 or

θ = 30⁰ i.e. wind is blowing at 5√5 ms^-1 30⁰ North of east.