# How can the speed of a car rolling down a valley be calculated without gas?

• port31
In summary: Another way would be to use the g value from the book and use the equation v = mgh to find the final speed.
port31

## Homework Statement

A 1500kg car traveling at 10m/s suddenly runs out of gas while approaching a valley.
The car is 10m above the valley floor when it starts to coast down the valley.
the gas station is 15meters above the valley floor on the other side.
How fast will the car be going as it coasts to the gas station on the other side?

## The Attempt at a Solution

the car is going 10m/s when it coasts and is 10m above the valley floor so it should reach the other side 10m high with a speed of 10m/s. so it will have that much energy to go 5 more meters up to the gas station.
so i set it up like this
$\frac{m{v_i}^2}{2}-mgh=\frac{m{v_f}^2}{2}$
when I do this i get that the final speed is zero. but my book says it is 1.41m/s

port31 said:

## Homework Statement

A 1500kg car traveling at 10m/s suddenly runs out of gas while approaching a valley.
The car is 10m above the valley floor when it starts to coast down the valley.
the gas station is 15meters above the valley floor on the other side.
How fast will the car be going as it coasts to the gas station on the other side?

## The Attempt at a Solution

the car is going 10m/s when it coasts and is 10m above the valley floor so it should reach the other side 10m high with a speed of 10m/s. so it will have that much energy to go 5 more meters up to the gas station.
so i set it up like this
$\frac{m{v_i}^2}{2}-mgh=\frac{m{v_f}^2}{2}$
when I do this i get that the final speed is zero. but my book says it is 1.41m/s

Perhaps the book used a g value of 9.8 rather than 10 ?

ya i just realized that. you that seems to be the problem. so my setup is correct.

Hi port 31 , welcome to PF!

Loks like the book used g =9.8m/s^2 and you used g = 10m/s^2. I'd say you are both correct. Considering that with friction and air drag always present, you're not going to make it up the hill anyway.

cragar said:
ya i just realized that. you that seems to be the problem. so my setup is correct.

Your set up was certainly one way of doing it.

## 1. What factors affect the speed of a car rolling down a valley?

The speed of a car rolling down a valley is affected by several factors, including the slope of the valley, the weight and size of the car, and any external forces such as wind or friction. The angle of the slope is a major factor, as a steeper slope will result in a faster descent. The weight and size of the car also play a role, as a heavier and larger car will have more momentum and thus a higher speed. External forces can also impact the speed, as wind can either push the car forward or slow it down, and friction from the surface of the valley can either assist or hinder the car's movement.

## 2. How does the shape of the valley affect the movement of a rolling car?

The shape of the valley can greatly impact the movement of a rolling car. A smooth, concave valley will allow the car to roll smoothly and gain speed, while a bumpy or uneven valley may slow down or even stop the car's movement. The angle of the slope and any curves in the valley can also affect the direction of the car and how it moves.

## 3. What is the role of gravity in a car rolling down a valley?

Gravity is the force that pulls the car down the slope of the valley. The steeper the slope, the stronger the force of gravity and the faster the car will descend. Gravity is also responsible for the car's acceleration as it gains speed while rolling down the valley.

## 4. Can a car roll up a valley?

In most cases, a car cannot roll up a valley. This is because the force of gravity is pulling the car down the slope, making it difficult for the car to move in the opposite direction. However, if the car has enough momentum or is aided by an external force, it may be able to roll up a slight incline in the valley.

## 5. How does the surface of the valley impact the movement of a rolling car?

The surface of the valley can greatly affect the movement of a rolling car. A smooth and even surface will allow the car to roll smoothly and quickly, while a rough or uneven surface may slow down or even stop the car's movement. Different surfaces, such as grass or gravel, can also impact the car's traction and how it moves down the valley.

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