# Car rolling down a valley

1. Jul 20, 2012

### port31

1. The problem statement, all variables and given/known data
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?
3. 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

2. Jul 20, 2012

### PeterO

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

3. Jul 20, 2012

### cragar

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

4. Jul 20, 2012

### PhanthomJay

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.

5. Jul 20, 2012

### PeterO

Your set up was certainly one way of doing it.