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? (a) 0.63m/s2 directed 55∘ south of west (b) 0.44m/s2 directed 24∘ south of west (c) 0.77m/s2 directed 35∘ south of west (d) 0.77m/s2 directed 55∘ south of west (e) 1.1m/s2 directed 35∘ south of west

The required magnitude of acceleration is at 55 degrees from south of west. Hence, option (c) is correct.

Given data:

The mass of object is, m = 27 kg.

The magnitude of force towards the south is, F = 12 N.

The magnitude of force towards the west is, F' = 17 N.

Here we will follow the Newton's second law that applied force will cause to accelerate the object along the same direction.

Then net force is,

Now, the direction will be,

This is the direction of 55 degrees towards south. So, acceleration will be towards south of west.

Then,

Thus, we can conclude that the required magnitude of acceleration is at 55 degrees from south of west. Hence, option (c) is correct.

Learn more about the Newton's second law here:

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(c) 0.77 m/s^2 directed 35° south of west.

Explanation:

Let's first find the resultant force and its direction:

F = 20.808 N

To find the direction, we can just imagine the forces as lengths of a right angled triangle.

So, Force (west) will be our perpendicular.

and Force (south) will be our base.

Calculating the angle we have:

Theta = 54.78°    (angle from south)

Direction of resultant force = 90 - 54.78 = 35.22° (south of west)

Taking out the acceleration, we get:

F = m * a

20.808 = 27 * a

a = 0.77 m/s^2

So the answer is (c)

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