Final answer:
To find the average drag force exerted on the car, one needs to use the work-energy theorem, converting the units accordingly, and then calculate the work done against gravity and the change in kinetic energy.
Step-by-step explanation:
To determine the magnitude of the average drag force exerted on the car as it coasts up the exit ramp, we need to apply the work-energy theorem. This theorem relates work done to the change in kinetic energy. We'll first convert the car's weight from kN to N (1 kN = 1000 N), and its speeds from mph to m/s.
Then we'll calculate the initial and final kinetic energies and the potential energy gained due to elevation change. The difference in kinetic energy, plus the potential energy gained, equals the work done against drag.
First, we calculate the work done against gravity which is the car's weight multiplied by the height (W = mgh). Then, the difference in kinetic energy (ΔKE) is the final kinetic energy (KEf) minus the initial kinetic energy (KEi). The work done by the drag force plus the work done against gravity equals the total work done on the car.
Using the work-energy theorem, we can set up the equation:
Wdrag + Wgravity = ΔKE
The average drag force (Fdrag) can be found by dividing the work done by the drag force (Wdrag) by the displacement (362 m). Wdrag is the total work minus the work done against gravity.
F_drag = (1/2) × 73.1 × 10³ kg × ((25.8 m/s)² - (12.1 m/s)²) + 73.1 × 10³ kg × 9.81 m/s² × (14.9 m - 0 m) / 362 m
F_drag ≈ 4.28 × 10⁶ J / 362 m
F_drag ≈ 11823 N
Therefore, the magnitude of the average drag force exerted on the car is approximately 11,823 N.