Problem Involving The Conservation Of Energy

[Pat2666]

I have another problem I need some help with.

Here's the problem :

A 51.1 kg child slides down a water slide with a velocity of 0.9 m/sec at the top. At the bottom of the slide, she is moving horizontally, y=2.5 meters above the water. She splashes into the water d=3 meters to the left of the bottom of the slide.
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a) Assuming potential energy to be zero at the water level, what is the mechanical energy of the child at the top of the slide?
MEo= J
1704 J
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b) How high is the top of the slide above the bottom of the slide?

As shown I was able to find out the mechanical energy of the child at the top of the slide (1704J) but I can't seem to figure out how to solve for the height of the slide.

I would have thought that you just set KE + PE = 1704 and solve for h, which I did and got 3.36m, but it isn't the right answer :(

So I did .5(51.1kg)(.9m/s)^2 + 51.1kg(9.81m/s^2)h = 1704J

I'm stumped as I don't see any other way of solved for the height. Any help would be appriciated. :)

 

[alphysicist]

Hi Pat2666,

The potential energy is zero at the water's surface, so that's where h=0 at. So when you found that h=3.36m, that means the slide is that far above the water's surface.

However, although that will help to answer part b, that's not quite what part b was asking for.

 

[Pat2666]

Well it's not really asking for the total height is it? Just the height of the top of the slide to the end of it no? I tried adding 3.36m to the 2.5m above water just to see if I misread the question, but it was still wrong.

 

[alphysicist]

The top of the slide is 3.36 m above the water, the bottom of the slide is 2.5 meters above the water. The question is asking for how far the top of the slide is above the bottom of the slide. What would that be?

 

[Pat2666]

OMG I'm so dumb! Thank you lol

I kept thinking that what I was solving for was h, rather than h + the additional height.

Thanks so much! I've been working on this problem forever!

 

[alphysicist]

Sure, glad to help!