Three forces acting on an object are given by F1 = (-8.79i + 8.34j) N, F2 = (7.06i + -3.02j) N, and F3 = (-3.05i) N. The object experiences an acceleration of magnitude 2.26 m/s2. What are the components of the acceleration vector?

The net force is -4.78i +5.22j. Its magnitude is

{F} = sqrt[(-4.78)^2 + 5.22^2] = 7.08 N. The mass is therefore
|F|/a = 3.13 kg

For the acceleration vector, divide the force vector by the mass.

thanks a lot. that really helped.

To find the components of the acceleration vector, we need to apply Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

Since we have three forces acting on the object, we need to find the net force first. The net force can be calculated by summing up all the individual forces. Let's add the given forces:

F_net = F1 + F2 + F3

F_net = (-8.79i + 8.34j) N + (7.06i + -3.02j) N + (-3.05i) N

Now, we can calculate the net force vector:

F_net = (-8.79i + 7.06i - 3.05i) N + (8.34j - 3.02j) N

F_net = (-4.78i + 5.32j) N

Now, we can apply Newton's second law to find the acceleration vector. According to the equation F_net = m * a, where m is the mass of the object and a is the acceleration vector, we can rearrange the equation as follows:

a = F_net / m

To find the components of the acceleration vector, we need to divide the net force vector by the magnitude of the acceleration:

a = (F_net / ||F_net||) * ||a||

where ||F_net|| represents the magnitude of the net force vector, and ||a|| is the given magnitude of the acceleration.

Given that the magnitude of the acceleration is 2.26 m/s^2, we can calculate the components of the acceleration vector.

||F_net|| = sqrt((-4.78)^2 + (5.32)^2) N

||F_net|| ≈ 6.97 N

Now, we can find the components of the acceleration vector:

a = (F_net / ||F_net||) * 2.26 m/s^2

a = ((-4.78i + 5.32j) N / 6.97 N) * 2.26 m/s^2

a ≈ (-1.74i + 1.93j) m/s^2

Therefore, the components of the acceleration vector are approximately -1.74 m/s^2 in the x-direction (i) and 1.93 m/s^2 in the y-direction (j).