Question

A novice golfer on the green takes three strokes to sink the ball .The successive displacement of the ball are 4.00 m to the north 2.00 m northwest and 1.00 m at 30.0 west of south .starting at the same initial point an expert golfer could make the hole in which single displacement.

Answer 1

$$\bold{s}=(0,4)+(2\cos{45},2\sin{45})+(\sin{30},-\cos{30})$$

$$\bold{s}=(1.914,4.548)m$$

Magnitude:

$$s=\sqrt{1.914^2+4.548^2}=4.93\ m$$

$$\theta=\arctan{\frac{1.914}{4.548}}=22.8\degree \text{W of N}$$