Physics Problem


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An Olympic runner leaps over a hurdle. If the runner's initial vertical speed is 2.2 m/s, how much will the runner's center of mass be raised during the jump?

Force of gravity is 9.81m/s^2

now would it just be 9.81 x 2.2 = 21.6

? Im kinda stuck on this one

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Okay, it's been a few years since I've done this sort of physics. I think this is how you go about doing it though.

First off, you can either look in a book, or derive the equation which relates position, acceleration and velocity. You get something that looks like:

X - Xo = Vo[(V-Vo)/a] + 0.5a[(V-Vo)/a]^2

where Xo and Vo are the initial displacement and velocity, respectively. ^2 means squared, and / is used for division.

We're given a few numbers in the question. Xo will be 0, and Vo will be 2.2m/s.

We also know V, because of the physics of the problem. We're trying to find the height of the runner, which happens when the verticle velocity is zero. Think about it for a second, if you're vertical motion is stopped, you're not going any higher, right? And if it's negative, you're on your way down. So set V = 0.

A, being gravity (the only vertical acceleration in the question, I assume) of course is -9.81 m/s^2. I'll denote it as g.

Now we have something a bit simpler, at

x = -[Vo^2 + Vo(0.5)]/g

Remember that g is given as a negative number, which will make our result positive (which is what we want.)

So, plug in the numbers and see what you get. I get ~ 0.61m

Feel free someone to correct me if I'm wrong, but I think I did this one okay.

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