A police officer in hot pursuit drives her car through a circular turn of radius 305 m with a constant speed of 83.5 km/h. Her mass is 55.0 kg. what are the magnitude and the angle of the net force of the officer on the car seat?

There must be a vertical force M g to balance her weight and a horizontal force M V^2/R to provide the centripetal acceleration.

Use the Pythagorean theorem for the magnitude, and the force ration for the tangent of the angle.

To find the magnitude and angle of the net force on the police officer in the car seat, we can use 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.

First, let's convert the speed from km/h to m/s:
83.5 km/h * (1/3.6) m/s = 23.2 m/s

Next, we need to find the acceleration of the police officer. Since the car is moving in a circular path, it is experiencing centripetal acceleration. The formula for centripetal acceleration is given by:

a = v² / r

where:
a = centripetal acceleration
v = velocity
r = radius

Plugging in the values:
a = (23.2 m/s)² / 305 m
a ≈ 1.77 m/s²

Now, we can calculate the net force acting on the police officer using Newton's second law:

F = m * a

where:
F = net force
m = mass
a = acceleration

Plugging in the values:
F = (55.0 kg) * (1.77 m/s²)
F ≈ 97.35 N

So, the magnitude of the net force of the police officer on the car seat is approximately 97.35 N.

To find the angle of the net force, we need to consider the direction of the net force relative to the velocity of the car. Since the net force is acting towards the center of the circular path (centripetal force), the angle between the net force and the velocity is 90 degrees.

Therefore, the angle of the net force of the police officer on the car seat is 90 degrees.