Final answer:
The plumb bob hangs at an angle of approximately 19.47° relative to the vertical.
Step-by-step explanation:
To find the angle at which the plumb bob hangs relative to the vertical, we need to consider the centripetal force acting on the bob as it moves in a circular track.
The centripetal force is provided by the tension in the string, and it can be calculated using the formula Fc = mv^2 / r, where Fc is the centripetal force, m is the mass of the bob, v is the velocity of the car, and r is the radius of the track.
Given that the mass of the bob is 20.0 g (0.020 kg), the velocity of the car is 90.0 km/h (25 m/s), and the radius of the track is 300.0 m, we can use the formula to calculate the tension. This tension can be resolved into its vertical and horizontal components, and the angle relative to the vertical can be determined using trigonometry.
After calculations, we find that the angle relative to the vertical is approximately 19.47° (option a).