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183_notes:examples:positionpredict [2014/07/10 19:55] – [Solution] caballero | 183_notes:examples:positionpredict [2014/07/11 13:45] – [Setup] caballero | ||
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* The location of the cart can be predicted using the position update formula, $\vec{r}_f = \vec{r}_i + \vec{v}_{avg} \Delta t$ | * The location of the cart can be predicted using the position update formula, $\vec{r}_f = \vec{r}_i + \vec{v}_{avg} \Delta t$ | ||
* The motion of the cart is represented using the following motion diagram. | * The motion of the cart is represented using the following motion diagram. | ||
+ | {{url> | ||
==== Solution ==== | ==== Solution ==== | ||
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$$\vec{r}_f = \vec{r}_i + \vec{v}_{avg} \Delta t = \vec{r}_i + \vec{v}_{cart} \Delta t = \vec{r}_i + \langle 1.2, 0, 0 \rangle \dfrac{m}{s} (3 s) = \vec{r}_i + \langle 3.6, 0, 0 \rangle m$$ | $$\vec{r}_f = \vec{r}_i + \vec{v}_{avg} \Delta t = \vec{r}_i + \vec{v}_{cart} \Delta t = \vec{r}_i + \langle 1.2, 0, 0 \rangle \dfrac{m}{s} (3 s) = \vec{r}_i + \langle 3.6, 0, 0 \rangle m$$ | ||
- | You might use the video to define an origin such that the initial position of the cart is $\vec{r}_i = \langle 0.4, 1.1, 0 \rangle m$. With that new information, | + | You might use the video to define an origin such that the initial position of the cart is $\vec{r}_i = \langle 0.4, 1.1, 0 \rangle m$. With that new information, |
- | $$\vec{r}_f = \vec{r}_i + \langle 3.6, 0, 0 \rangle m = \langle 0.4, 1.1, 0 \rangle m + \langle 3.6, 0, 0 \rangle m = \langle 4.0, 1.1, 0, \rangle m$$. | + | $$\vec{r}_f = \vec{r}_i + \langle 3.6, 0, 0 \rangle m = \langle 0.4, 1.1, 0 \rangle m + \langle 3.6, 0, 0 \rangle m = \langle 4.0, 1.1, 0 \rangle m$$. |
- | Notice that $y$-position remained unchanged because all the motion of the cart was in the $x$-direction. | + | Notice that $y$-position |