Resultant Vector of Typhoon YolandaVector x-component y-component425 km E SE Identify the velocity of Typhoon Yolanda as it enters and exit the Philippine Area of Responsibility

The given velocities are:

v₁ = 425 km/h SE

v₂ = 64 km/h W

v₃ = 241 km/h W

v₄ = 34 km/h W

v₅ = 250 km/h W

v₆ = 314 km/h W

v₇ = 78 km/h W

v₈ = 314 km/h W

v₉ = 298 km/h W

Here

V = v₂ + v₃ + ....+ v₉

V = 64+241+34+250+314+78+314+298

V = 1593km/h

Vector component along X axis (East):

V_x = v₁cos45° - V

V_x = 425cos45° - 1593

V_x = -1292.480 km/h

or

V_x = 1292.480 km/h (along West)

Vector component along Y axis (North):

V_y = -v₁sin45°

V_y = -425sin45°

V_y = -300.520 km/h

or

V_y = 300.520 km/h (along the South)

theta = tan^-1(V_y/V_x)

theta = tan^-1(300.52/1292.48)

theta = 13.089° South of West (with -X axis)

or

theta = (180+ 13.089)° with X axis

theta = 193.089° with X axis

V = √{V_x² + V_y²}

V = √{1292.48² + 300.52²}

V = 1326.96 km/h