Question

A boat is sailing 6.17 m/s directly cast across the harbor when a gust of wind comes up, the boat changes its direction to 11.0°, north of cast and its speed increases to 7.2 m/s. What is the change in velocity of the boat?

Answer 1

$$\Delta \vec{v}=(7.2\cos{11},7.2\sin{11})-(6.17,0)$$

$$\Delta \vec{v}=(0.898,1.374)\frac{m}{s}$$

$$\Delta v=\sqrt{0.898^2+1.374^2}=1.64\frac{m}{s}$$

Direction:

$$\theta=\arctan{\frac{1.374}{0.898}}=56.8\degree N\ of\ E$$