Final answer:
The magnitude and direction of the average force that acted on the object can be determined by using the principles of Newton's second law. The average force is equal to the mass of the object multiplied by the change in velocity over the given time interval.
The magnitude of the change in velocity can be determined by using the Pythagorean theorem. The direction of the change in velocity can be found using trigonometry.
The magnitude of the average force that acted on the object over the 2.00-s interval is 30.0 N (newtons) and the direction of the average force is 45.0° north of east.
Step-by-step explanation:
The magnitude and direction of the average force that acted on the object can be determined by using the principles of Newton's second law. The average force is equal to the mass of the object multiplied by the change in velocity over the given time interval. In this case, the change in velocity is from moving east at 15.0 m/s to moving northwest at 15.0 m/s. Since the direction changes from east to northwest, the change in velocity has both a magnitude and direction.
First, we need to calculate the change in velocity. The magnitude of the change in velocity can be determined by using the Pythagorean theorem:
Δv = √((15.0 m/s)^2 + (15.0 m/s)^2) = √(450 m^2/s^2 + 450 m^2/s^2) = √900 m^2/s^2 = 30.0 m/s
The direction of the change in velocity can be determined by using trigonometry. The angle between the initial velocity vector (east) and the final velocity vector (northwest) can be found:
θ = tan^(-1)((15.0 m/s) / (15.0 m/s)) = tan^(-1)(1) = 45.0°
Therefore, the magnitude of the average force that acted on the object over the 2.00-s interval is 30.0 N (newtons) and the direction of the average force is 45.0° north of east.