Question

An athlete running at the velocity of 23m/s due east is confronted with two trade winds. One wind traveling at 10m/s in a direction of N65 degrees E and the other wind traveling at 8m/s in a direction S 70 degree E. Find the resultant velocity and direction of the athlete

Answer 1

$\upsilon_{we}=\upsilon_{1}-\upsilon_{2}\times cos65^o-\upsilon_{3}\times cos70^o=23-10\times 0.42-8\times 0.34=16.08$

$\upsilon_{sn}=\upsilon_{3}\times sin70^o-\upsilon_{2}\times sin65^o=8\times 0.94-10\times 0.9=-1.48$

$\upsilon_{result}=\sqrt{\upsilon_{we}^2+\upsilon_{sn}^2}=\sqrt{16.08^2+(-1.48)^2}=$ 16.15

$\alpha=arccos\frac{\upsilon_{we}}{\upsilon_{result}}=arccos\frac{16.08}{16.15}=5.34^o$