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--- 183_notes:examples:positionpredict [2014/07/10 19:55] – [Solution] caballero
+++ 183_notes:examples:positionpredict [2014/07/11 13:47] – caballero
@@ Line 28: / Line 28: @@
   * 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.
+{{url>http://www.pa.msu.edu/~caballero/teaching/simulations/FanCartConstantVelocity.html 500px,550px|Simulation of Fan Cart moving with Constant Velocity}}
 ==== Solution ====
@@ Line 35: / Line 36: @@
 $$\vec{r}_f = \vec{r}_i + \vec{v}_{avg} \Delta t = \vec{r}_i + \vec{v}_{cart} \Delta t = \vec{r}_i + \langle 1.2, 0, 0 \rangle \dfrac{m}{s} (3 s) = \vec{r}_i + \langle 3.6, 0, 0 \rangle m$$
-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, the final location of the cart is,
+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, the final location of the cart can be computed exactly,
-$$\vec{r}_f = \vec{r}_i + \langle 3.6, 0, 0 \rangle m = \langle 0.4, 1.1, 0 \rangle m + \langle 3.6, 0, 0 \rangle m = \langle 4.0, 1.1, 0, \rangle m$$.
+$$\vec{r}_f = \vec{r}_i + \langle 3.6, 0, 0 \rangle m = \langle 0.4, 1.1, 0 \rangle m + \langle 3.6, 0, 0 \rangle m = \langle 4.0, 1.1, 0 \rangle m$$.
-Notice that $y$-position remained unchanged because all the motion of the cart was in the $x$-direction.
+Notice that $y$-position of the cart remained unchanged because all the motion of the cart was in the $x$-direction.