# Homework Help: If the height of the water slide is h = 3.2m and the person's initial

1. Aug 27, 2014

### Cody

"If the height of the water slide is h = 3.2m and the person's initial speed at point A (at the top of slide) is 0.54m/s, at what location does the swimmer splash down in the pool?"

I saw a thread with the same question back from 2005 but it is now closed.
I understand that you have to use conservation of energy at point A and at the bottom of the slide to find velocity at the bottom of the slide, then use the formula x = v√2y/g.

I am however confused with the following:
Why can I not substitute the exact values for h into the formula i.e
mgh + 1/2 mv^2 = mgh + 1/2 mv^2
since it is known, but rather have to use h-1.50(for the bottom) and 1.50(for the top)

Hope someone understands what I am asking.
Any help is appreciated.

2. Aug 27, 2014

### Staff: Mentor

You need to provide a diagram (or simply a link to the original problem). Or at least describe the slide in more detail.

What matters when calculating the velocity at the bottom of the slide is Δh. So as long as you get that right, your proposed method should work fine.

You can use any point as your reference level, where y = 0.

3. Aug 27, 2014

### Cody

Found out how to attach a link. here's the picture

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Last edited: Aug 27, 2014
4. Aug 27, 2014

### Zondrina

Find the change in potential energy from the top of the slide to the bottom. Use this to find the final speed of the girl.

We can worry about where she lands afterwards.

5. Aug 27, 2014

### Staff: Mentor

Good.

I have no idea why you think you have to use this (which is wrong, by the way).

The diagram shows the height of the bottom of the slide to be 1.50 m; the height at the top is that plus an additional "h".

6. Aug 28, 2014

### Cody

This is the solution I have. If I substitute the exact values for h (i.e. 1.50 at the bottom of the slide and 3.2 at the top), I don't get the same answer. I don't know if I am doing something wrong or if you just cannot substitute the exact values for h into your equation, but rather have to use h+1.50 and h.

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7. Aug 28, 2014

### Staff: Mentor

I think you are getting confused about the meaning of "h" in this problem. Here, h is simply the change in height of the slide from top to bottom; h is not the distance from the top of the slide to the water level.

In your formula for potential energy, use $mgy$ instead of $mgh$, where "y" is the vertical position measured from the water level. $y_A$ ≠ 3.2. (h = 3.2)

Your first job is to figure out what $y_A$ and $y_B$ equal.