# Calculating the stopping distance of a car sliding down an incline.

1. Oct 19, 2012

### waqaszeb

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

When a car is traveling at 22 m/s on level ground, the stopping distance is found to be 22 m. This distance is measured by pushing hard on the brakes so that the wheels skid on the pavement. The same car is driving at the same speed down an incline that makes an angle of 7.8° with the horizontal direction. What is the stopping distance now, as measured along the incline?

2. Relevant equations

v^2 + v(i) + 2a (delta x)

3. The attempt at a solution

Here's my weak line of reasoning: I used the above equation to find the acceleration since the stopping distance for the first case is known. Then I calculated a(net) for that same acceleration for the second case because I assumed that when skidding down an incline the acceleration is basically the same as when there is no incline except this time is an cos and sin component. Then I plugged back the new acceleration into the same equation to get delta x (stopping distance) for the incline. I think I got this wrong because there is kinetic friction involved in this problem. I just can't seem to calculated the forces associated with F(k) due to the limited amount of information given.

2. Oct 19, 2012

### PhanthomJay

For the level road case, since you know the acceleration, you can determine the kinetic friction coefficient using Newton 2 after drawing your free body diagram. Always draw free body diagrams to identify forces acting and apply Newton's laws.

Now draw the FBD for the car on the incline, and solve for the new a along the incline. And then solve for the distance.