# Maximum speed of car on downhill

• Jack122
In summary, the exercise given is incorrect and nonsensical. The power of the car on flat ground and on uphill terrain should be the same, but the given values do not allow for this. Additionally, the question mentions friction force, but it is more likely referring to rolling resistance instead.
Jack122

## Homework Statement

The exercise is this: The mass of the car is m=500 kg. The maximum speed of the car on flat road is v1=35 m/s and on 10 % up hill (tan(alpha)=0.1, alpha is with respect to flat) the maximum speed is v2=20 m/s. The friction force is double on up hill because it has been made with different material. What is the maximum speed of the car on down hill (5%) when the road is made with the same material than the flat surface? Suppose that the air resistance is zero.

## Homework Equations

P=F*v
Gx=mg sin(alpha)
F_f=friction force

## The Attempt at a Solution

I think the exercise itself is not correct. The power of the car on flat is P1=(F_f)v1 and on up hill it is P2=(2(F_f)+mg sin(alpha))v2. The powers need to be the same. So when I solve for F_f I get F_f=(mg sin(alpha)v2)/(v1-2v2) and this is smaller than zero because v1-2v2=(35-2*20) m/s=-5 m/s and mg sin(alpha)v2 is greater than zero (sin(alpha)=sin(arctan(0.1))=0.0995). But the friction force needs to be greater than zero. So I think this is incorrect exercise because the car cannot produce enough power to climb that hill with that speed.

I agree with you. Maybe it meant to say the friction is double on the flat?

There is another reason the question is nonsense. Friction between road and tyre does not impede the progress of the vehicle. In the present case that is static friction. No work is required to overcome it. Indeed, without it the hill could not be climbed. Presumably the question means rolling resistance, not friction.

## 1. What is the maximum speed a car can reach when going downhill?

The maximum speed a car can reach when going downhill depends on various factors such as the slope of the hill, the weight of the car, and the condition of the road. However, most cars can reach speeds of up to 60-70 miles per hour when going downhill.

## 2. Can a car go faster than its maximum speed when going downhill?

Technically, yes, a car can go faster than its maximum speed when going downhill. However, this is not recommended as it can be unsafe and put the driver and others on the road at risk.

## 3. How does gravity affect the maximum speed of a car on downhill?

Gravity plays a significant role in determining the maximum speed of a car on downhill. As the car goes down the hill, gravity pulls it downwards, increasing its speed. However, if the slope is too steep, gravity can also cause the car to lose control, so it is essential to drive at a safe and controlled speed.

## 4. Can the maximum speed of a car on downhill be affected by the type of tires?

Yes, the type of tires can significantly impact the maximum speed of a car on downhill. Tires with a higher speed rating and better traction can handle higher speeds and maintain control on steep slopes, while worn-out or low-quality tires can cause the car to lose control at high speeds.

## 5. Is it safe to drive at maximum speed when going downhill?

No, it is not safe to drive at maximum speed when going downhill. It is essential to maintain a safe and controlled speed, especially on steep slopes, to avoid accidents or losing control of the car. It is always better to prioritize safety over speed when driving downhill.

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