Final answer:
The choice of speed when driving down a steep downgrade on a banked curve should be influenced by the banking angle of the road, which determines the ideal speed to negotiate the curve without friction. Steeper angles enable higher speeds, but the ideal speed must align with the angle to maintain control using centripetal force.
Step-by-step explanation:
When driving down a steep downgrade or taking a tight curve on a steeply banked track, your choice of speed should be influenced by the physics of banked curves. Ideally, the road's angle, known as the banking angle, determines the ideal speed at which the curve can be negotiated without relying on friction. For instance, if you calculate the ideal speed for a 100 m radius curve banked at 65.0° on a frictionless road, you'll find that this speed allows a car to make the curve due solely to the banking angle and the centripetal force. A similar calculation can be applied to a less steep angle, such as a 15.0° banked curve, to find both the ideal speed and the minimum coefficient of friction needed for a slower speed.
The answer to the question of what influences the choice of speed on a steep downgrade is not just the road's slope but also the physics of the curve's banking. When driving down a steep downgrade, if the curve is not banked, then friction between the tires and the road surface will play a crucial role in maintaining control. Conversely, a steeply banked curve allows one to rely less on friction and more on the centripetal force due to the banking angle to maintain control.