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

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A car traveling at 25.43 m/s on a 17° slope will coast uphill until its kinetic energy is fully converted to potential energy. To determine how far it will coast, a free body diagram should be drawn to analyze the forces acting on the car, particularly the gravitational force acting down the slope. The downward acceleration due to gravity can be calculated, and kinematic equations can be applied to find the distance traveled until the car comes to a stop. The solution involves equating the initial kinetic energy to the potential energy gained at the highest point. Ultimately, this approach will yield the distance the car coasts up the hill before rolling back down.
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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?

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The Attempt at a Solution

 
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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.
 

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