Final answer:
To find the magnitude of the object's final velocity, calculate the change in velocity caused by the force using Newton's second law and equation of motion. Plugging in the given values, we find that the object's final velocity is approximately 28.5 m/s.
Step-by-step explanation:
To find the magnitude of the object's final velocity, we need to calculate the change in velocity caused by the force acting on it. The force is acting towards the east, so it will change the object's initial northward velocity.
First, we calculate the change in velocity caused by the force using Newton's second law: F = ma. Rearranging the formula to solve for acceleration, we get a = F/m.
Plugging in the values, we get a = 15 N / 3.00 kg = 5 m/s².
Next, we calculate the change in velocity caused by the force using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Plugging in the values, we get v = 15 m/s + (5 m/s²)(2.70 s). Solving the equation, we find v ≈ 28.5 m/s.