Driving the Perfect Curve: Maximum Speed on a Hilltop

In summary, the maximum speed at which a person can drive a car over the top of a hill without the car leaving the road is √rg, where r is the radius of the hill and g is the acceleration of gravity. The normal force must be equal to zero for this maximum speed to occur.
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A person drives a car over the top of a hill, the cross section of which can be approximated by a circle of radius r=250m. What is the greatest speed at which he can drive without the car leaving the road at the top of the hill?

I know that the maximum speed occurs when the normal force= zero. And by my calculations vmax=√rg (where r is the radius and g is the acceleration of gravity)

Is this all I need? Am I missing anything?
 
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  • #2
Seems ok to me. What to you think you might be missing?
 
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I didn't think there was anything missing, this is just me being paranoid I guess. Thank you
 

What is "Driving the Perfect Curve: Maximum Speed on a Hilltop"?

"Driving the Perfect Curve: Maximum Speed on a Hilltop" is a study that examines the optimal speed and trajectory for driving around a curve on a hilltop in order to achieve the maximum speed.

Why is it important to study the perfect curve on a hilltop?

Understanding the perfect curve on a hilltop can help improve driving techniques and safety. It can also provide insights into the physics of driving and how to optimize speed and control on different terrains.

How is this study conducted?

This study typically involves using a combination of mathematical equations and computer simulations to analyze the factors that affect the maximum speed on a hilltop curve, such as the angle of the hill, the radius of the curve, and the car's velocity.

What are some key findings of this study?

The results of this study may vary depending on the specific parameters and conditions, but generally, it has been found that a shallower hill with a larger radius curve allows for a higher maximum speed. Additionally, a smooth and gradual acceleration and deceleration can help maintain a higher speed throughout the curve.

How can the findings of this study be applied in real-life situations?

By understanding the optimal speed and trajectory for driving on a hilltop curve, drivers can improve their performance and safety on the road. This knowledge can also be used in the design and construction of roads and highways to ensure safer and more efficient driving conditions.

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