How Far Will a Car Coast Up a Hill After Running Out of Gas?

[mcryder16]

Homework Statement

A car traveling at 25.43 m/s runs out of gas while traveling up a 17° slope. How far up the hill will it coast before starting to roll back down?

Homework Equations

Not sure on the equation to be used?

The Attempt at a Solution

 

[nickjer]

Draw a free body diagram of the car and solve for the downward acceleration of gravity. Then just use kinematics to solve for when the velocity is 0.

 

[nlightner]

Kinematics in one dimension deals with the motion of objects along a straight line. To solve this problem, we can use the equation for displacement in one dimension, which is d = v0t + 1/2at^2, where d is the displacement, v0 is the initial velocity, a is the acceleration, and t is the time. In this scenario, the car's initial velocity is 25.43 m/s and the acceleration due to gravity is 9.8 m/s^2. Since the car runs out of gas, there is no external force acting on it and therefore, the acceleration is 0 m/s^2. We can rearrange the equation to solve for t, which gives us t = (2d/v0)^1/2. Using the given information, we can calculate the time it takes for the car to stop moving up the slope. Then, using this time, we can calculate the distance traveled using the same equation. The distance traveled up the hill before the car starts to roll back down will be equal to the distance traveled while coasting, which can be calculated using the equation d = v0t. Therefore, to answer the homework statement, we need to plug in the values for v0, t, and a (which is 0) into the equation d = v0t. This will give us the distance traveled up the hill before the car starts to roll back down.