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Hello,

I am new to this site. I am currently active duty military (navy) and I am trying to teach myself physics because when I get the time, I would like to take some college physics classes. I downloaded a few physics books online and I am trying to page through them. I am having some trouble figuring out this problem. I feel like a complete idiot because I have the correct answer right in front (teacher solution manual downloaded too) of me and still can't figure it out! Anyways, here is the problem and the correct answer (below). Any help you can offer would be appreciated.

An object falls freely from height h. It is released at time

zero and strikes the ground at time t. (a) When the object

is at height 0.5h, is the time earlier than 0.5t, equal to 0.5t,

or later than 0.5t? (b) When the time is 0.5t, is the height

of the object greater than 0.5h, equal to 0.5h, or less than

0.5h? Give reasons for your answers.

I understand the formula h=1/2gt^2, but what I don't understand is where they are getting the "0.707t" when they plug in 0.5h.

I also don't understand the second equation where they are getting 0.25h

I am new to this site. I am currently active duty military (navy) and I am trying to teach myself physics because when I get the time, I would like to take some college physics classes. I downloaded a few physics books online and I am trying to page through them. I am having some trouble figuring out this problem. I feel like a complete idiot because I have the correct answer right in front (teacher solution manual downloaded too) of me and still can't figure it out! Anyways, here is the problem and the correct answer (below). Any help you can offer would be appreciated.

## Homework Statement

An object falls freely from height h. It is released at time

zero and strikes the ground at time t. (a) When the object

is at height 0.5h, is the time earlier than 0.5t, equal to 0.5t,

or later than 0.5t? (b) When the time is 0.5t, is the height

of the object greater than 0.5h, equal to 0.5h, or less than

0.5h? Give reasons for your answers.

## Homework Equations

## The Attempt at a Solution

I understand the formula h=1/2gt^2, but what I don't understand is where they are getting the "0.707t" when they plug in 0.5h.

I also don't understand the second equation where they are getting 0.25h

**4. Answer**

With h=1/2gt^2

(a)0.5h=1/2g(0.707t)^2

(b)The distance fallen is 0.25h=1/2g(0.5t)^2. The elevation is 0.75h, greater than 0.5h.With h=1/2gt^2

(a)0.5h=1/2g(0.707t)^2

(b)The distance fallen is 0.25h=1/2g(0.5t)^2. The elevation is 0.75h, greater than 0.5h.

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