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So there is this question i've been having trouble with for the past hour. It involved a child going down a ramp on a sled at and angle theta with a total system of mass. accelerates down a hill of length L during a time interval delta t. (this is literally all the question gives you, other than a really simple diagram which only indicates where the 0 is located)

So far I've figured out that a = gsin0.

The question it's asking me is the magnitude of the child's velocity is. (choices) The correct choice is e which is sqrt(gLsin0/2) How do they end up with this?

Any help would be appreciated.

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  • $\begingroup$ Using a zero as a theta is confusing. If you don’t know MathJax yet and can’t write $\sin{\theta}$, I suggest just writing it out as “sin(theta)”. $\endgroup$ – G. Smith Jan 5 at 21:48
  • $\begingroup$ Your title indicates that you actually want the average speed, but your explanation makes it sound like you want the speed at the bottom of the hill. $\endgroup$ – G. Smith Jan 5 at 21:58
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First of all you know the acceleration due to gravity is g ($9.81 \frac{m}{s^2}$).

Next you know, ignoring friction on the slide and air resistance, all masses have the same vertical acceleration g in a gravitational field.

Then you know the acceleration of the child is as a function of g, $a=gsin$.

Next, you know from kinematics that the distance traveled, which is $L$, is given by

$L=\frac{at^2}{2}$

From that you can calculate the time it takes the child to go distance $L$. Then finally you can calculate the velocity from

$v=at$

The answer they gave you is probably just a combination of these steps.

Hope this helps.

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