Find velocity problem?

Question

A man was running due east at 5ms when a southwesterly wind blowing at 2ms changes both his speed and direction in which he was running. Calculate his new velocity? (magnitude and direction)

Answer 1

First, draw the vectors for the man (A) and the wind (B).

(I've left out the basic trig steps here)

Ry = Ay + By = 0 m/s + sqrt(2) m/s = sqrt(2) m/s ↓

Rx = Ax + Bx = 5 m/s + -sqrt(2) m/s ≈ 3.59 m/s →

Find the resultant (which will be the final speed):

R² = (Ry)² + (Rx)²

R = sqrt[(Ry)² + (Rx)²] = sqrt{ [sqrt(2) m/s]² + [3.59 m/s]² } = ...

Find the direction of the final speed as the angle below the horizontal:

tanθ = (Ry) / (Rx)  -->  ÃŽÂ¸ = tanˉ¹[(Ry)/(Rx)] = ...