From Mechanics

Revision as of 14:42, 14 May 2010 (edit) Ian (Talk | contribs) ← Previous diff		Current revision (14:56, 14 May 2010) (edit) (undo) Ian (Talk | contribs)
Line 1:		Line 1:
	We insert		We insert
	<math>t=0\ \text{s}</math>		<math>t=0\ \text{s}</math>
-	in the expression for the position vector to find the point where the frisby waqs thrown from.	+	in the expression for the position vector to find the point where the frisby was thrown from.
Line 7:		Line 7:
	& \mathbf{r}=\left( 5\times 0-{{0}^{2}} \right)\mathbf{i}+\left( 7\times 0 \right)\mathbf{j}+0\mathbf{k} \\		& \mathbf{r}=\left( 5\times 0-{{0}^{2}} \right)\mathbf{i}+\left( 7\times 0 \right)\mathbf{j}+0\mathbf{k} \\
	& \\		& \\
-	& =-24\mathbf{i}+56\mathbf{j}+0\mathbf{k}\ \text{m} \\	+	& =0\mathbf{i}+0\mathbf{j}+0\mathbf{k}\ \text{m}\\
	\end{align}</math>		\end{align}</math>
-	The point where the frisby was thrown is the origin. This is obtained by putting	+	Thus the point where the frisby was thrown from is the origin.
-	<math>t=0</math>	+
-	in the expression for	+	Using the result from part b)
-	<math>\mathbf{r}</math>	+
-	giving <math>\mathbf{r} =0\mathbf{i}+0\mathbf{j}+0\mathbf{k}\ \text{m}</math>.	+	<math>\begin{align}
		+	& \mathbf{r}=-24\mathbf{i}+56\mathbf{j}+0\mathbf{k}\ \text{m}
		+	\end{align}</math>
		+
		+	we get the distance from the origin to where it hits the ground is
		+
		+	<math>\sqrt{{{\left( -24 \right)}^{2}}+{{56}^{2}}}=\sqrt{576+3136}=\sqrt{3712}=60\textrm{.}9\ \text{m}</math>

---

Current revision

We insert \displaystyle t=0\ \text{s} in the expression for the position vector to find the point where the frisby was thrown from.

\displaystyle \begin{align} & \mathbf{r}=\left( 5\times 0-{{0}^{2}} \right)\mathbf{i}+\left( 7\times 0 \right)\mathbf{j}+0\mathbf{k} \\ & \\ & =0\mathbf{i}+0\mathbf{j}+0\mathbf{k}\ \text{m}\\ \end{align}

Thus the point where the frisby was thrown from is the origin.

Using the result from part b)

\displaystyle \begin{align} & \mathbf{r}=-24\mathbf{i}+56\mathbf{j}+0\mathbf{k}\ \text{m} \end{align}

we get the distance from the origin to where it hits the ground is

\displaystyle \sqrt{{{\left( -24 \right)}^{2}}+{{56}^{2}}}=\sqrt{576+3136}=\sqrt{3712}=60\textrm{.}9\ \text{m}