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correct. newtons second law gives the answer directly, provided the net force is calculated by vector addition of the two given forces. the direction of the net force gives the direction of the acceleration.
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
0.77 m/s² directed 55° south of west
0.44 m/s² directed 24° south of west
0.77 m/s² directed 35° south of west
1.1 m/s² directed 35° south of west

Explanation:

Step1: Calculate net - force magnitude

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

Step2: Calculate acceleration magnitude

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 direction of the net - force

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

Answer:

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