Only two horizontal forces act on a 3.0 kg body that can move over a frictionless floor. One force is 9.0 N, acting due east, and the other is 6.9 N, acting 54° north of west. What is the magnitude of the body's acceleration?

Add the two force vectors.

The components are:
East: 9.0 - 6.9 cos54 = 4.944 N
North: 6.0 sin 54 = 4.864 N

Then calculate the magnitude of the resultant.

sqrt[(4.944)^2 + (4.864)^2] = ___

Divide that by the mass to get the acceleration, in m/s^2.

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To find the magnitude of the body's acceleration, we first need to find the net horizontal force acting on the body.

Step 1: Resolve the 6.9 N force into its horizontal and vertical components.
The horizontal component of the force is given by:
horizontal component = 6.9 N * cos(54°)

Let's calculate the horizontal component:
horizontal component = 6.9 N * cos(54°) = 6.9 N * 0.5878 ≈ 4.05 N

Step 2: Calculate the net horizontal force.
The net horizontal force is found by adding the horizontal components of both forces:
net horizontal force = 9.0 N + 4.05 N = 13.05 N

Step 3: Use Newton's second law (F = ma) to find the acceleration.
The formula is rearranged to solve for acceleration:
acceleration = net horizontal force / mass

Let's calculate the acceleration:
acceleration = 13.05 N / 3.0 kg ≈ 4.35 m/s²

Therefore, the magnitude of the body's acceleration is approximately 4.35 m/s².

To find the magnitude of the body's acceleration, we need to calculate the net force acting on the body using the given forces.

First, let's resolve the second force into its horizontal and vertical components.

The vertical component (North-South direction) of the second force can be calculated using trigonometry:
Vertical component = 6.9 N * sin(54°)

Next, we'll add up the total horizontal and vertical components of the two forces:
Horizontal component = 9.0 N (since it's acting due east)

Now, we can calculate the net horizontal and vertical forces by adding up the components:
Net horizontal force = 9.0 N + (6.9 N * cos(54°))
Net vertical force = 6.9 N * sin(54°)

Since the floor is frictionless, there is no horizontal force opposing the motion. Therefore, the net horizontal force is the only force affecting the acceleration.

Finally, we can use Newton's second law of motion, F = ma, to find the magnitude of acceleration:
Net horizontal force = mass * acceleration
acceleration = Net horizontal force / mass

Substituting the values we calculated, we can find the magnitude of the body's acceleration.