Question

A duck has a mass of 2.5 kg. As the duck paddles, a force of 0.10 N acts on it in a direction due east. In addition, the current of the water exerts a force of 0.20 N in a direction of 52o south of east.

Determine the net force on the duck.
Determine the acceleration of the duck.

Answer 1

$$\vec{F_1}=(0.1, 0)\ N$$

$$\vec{F_2}=(0.2 \cos{52}, 0.2 \sin{52})\ N$$

The net force on the duck:

$$\vec{F}=\vec{F_1}+\vec{F_2}=(0.1+0.2 \cos{52}, 0.2 \sin{52})\ N$$

The magnitude:

$$F=\sqrt{(0.1+0.2 \cos{52})^2+(0.2 \sin{52})^2}=0.27\ N$$

The direction:

$$a=\arctan{ \frac{0.2 \sin{52}}{0.1+0.2 \cos{52}}}= 35^\circ$$

south of east.  

The acceleration of the duck:

$$a=\frac{F}{m}=\frac{0.27}{2.5}=0.11 \frac{m}{s^2}$$