If the only forces acting on a 3.0-kg mass are F1 = (3i - 8j) N and F2 = (5i + 3j) N, what is the magnitude of the acceleration (in m/s2) of the particle?Group of answer choices7.203.724.703.149.43

To solve this problem, we first need to find the net force acting on the mass. The net force is the vector sum of all the forces acting on the object.

The force F1 is given as (3i - 8j) N and the force F2 is given as (5i + 3j) N.

We add these two forces together to get the net force:

F_net = F1 + F2 = (3i - 8j) N + (5i + 3j) N = (3i + 5i) + (-8j + 3j) = 8i - 5j

So, the net force F_net = 8i - 5j N.

Next, we use Newton's second law, F = ma, where F is the net force, m is the mass, and a is the acceleration. We can rearrange this equation to solve for acceleration: a = F/m.

The magnitude of the acceleration is given by the magnitude of the net force divided by the mass:

a = |F_net| / m = sqrt((8^2) + (-5^2)) / 3.0 kg = sqrt(64 + 25) / 3.0 kg = sqrt(89) / 3.0 kg = 9.43 m/s^2

So, the magnitude of the acceleration of the particle is 9.43 m/s^2.