Question

two forces act on a moving object that has a mass of 27 kg. one force has a magnitude of 12 n and points due south, while the other force has a magnitude of 17 n and points due west. what is the acceleration of the object?
0.63 m/s² directed 55° south of west
0.44 m/s² directed 24° south of west
0.77 m/s² directed 55° south of west
0.77 m/s² directed 35° south of west
1.1 m/s² directed 35° south of west

Explanation:

Step1: Calculate the magnitude of the net - force

The two forces are perpendicular to each other. Using the Pythagorean theorem, the magnitude of the net - force $F_{net}$ is $F_{net}=\sqrt{F_1^{2}+F_2^{2}}$, where $F_1 = 17\ N$ (west - direction) and $F_2=12\ N$ (south - direction). So, $F_{net}=\sqrt{17^{2}+12^{2}}=\sqrt{289 + 144}=\sqrt{433}\approx20.81\ N$.

Step2: Calculate the acceleration

According to Newton's second law $F = ma$, where $m = 27\ kg$ and $F = F_{net}$. Then $a=\frac{F_{net}}{m}=\frac{20.81}{27}\approx0.77\ m/s^{2}$.

Step3: Calculate the direction of the net - force

Let $\theta$ be the angle of the net - force with respect to the west direction. Using the tangent function, $\tan\theta=\frac{F_2}{F_1}=\frac{12}{17}\approx0.7059$. Then $\theta=\arctan(0.7059)\approx35^{\circ}$ south of west.

Answer:

$0.77\ m/s^{2}$ directed $35^{\circ}$ south of west