How far will a car coast up a slope before rolling back down?

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A car traveling at 16.0 m/s on a 21.0-degree slope will coast up the hill before rolling back down. The initial calculation using energy conservation (1/2mv^2 = mgh) yields a height of 13.06 meters. However, to find the distance traveled up the slope, trigonometric functions must be applied. Specifically, using sin(21) = 13.06/x allows for the determination of the actual distance along the slope. The correct approach confirms that trigonometry is necessary for solving the problem accurately.
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A car traveling at 16.0 m/s runs out of gas while traveling up a 21.0 degree slope.

How far up the hill will it coast before starting to roll back down?

I tried

1/2mv^2=mgh
1/2(16)^2=9.8h
13.06=h

can anyone confirm if this is correct or not. I;m not sure if I have to use trig to solve this or not.

help please.
 
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looks good. the question is asking for the distance up the hill not just simply the height difference, so you'll have to use trig to find that.
 
si it would be sin(21)=13.06/x

x being the hyp/answer?
 
yea that was the answer
 

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