Question

A boat with a total mass of 500kg is traveling north on a lake. The motor of the provides a force of 400N in the northerly direction. The wind blows 30 degrees away from the northerly direction slightly towards east. it exerts a force of 300N on the boat. Find the acceleration of the boat including magnitude and direction. Assume friction between the boat and the water of the lake is negligible

Answer 1

Total force is (F₁=400, F₂=300)

$$F=\sqrt{F_1^2+F_2^2+2F_1F_2\cos30}=676.6 \, N$$

So the acceleration of the boat is a=F/m=1.35 m/s².

The cosine of an angle between the acceleration and the force F₁ is given by equation

$$\cos\alpha=\frac{F_1+F_2\cos 30}{F}=0.975$$

which correspond to $\alpha\simeq 13^\circ$ .

Answer. The acceleration of the boat is a=1.35 m/s² at an angle about 13 degrees towards east.