Solution 8.4c

From Mechanics

(Difference between revisions)
Jump to: navigation, search
(New page: We have <math>\mathbf{a}=4\mathbf{i}– 8\mathbf{j},\ \</math> <math>\mathbf{u}=4\mathbf{i}– 8\mathbf{j}\ \</math> and <math>\ \ \mathbf{ r}_{0}=6\mathbf{i}+2\mathbf{j}</math>. The ...)
Current revision (16:48, 13 April 2010) (edit) (undo)
 
(One intermediate revision not shown.)
Line 1: Line 1:
-
We have <math>\mathbf{a}=4\mathbf{i}– 8\mathbf{j},\ \</math> <math>\mathbf{u}=4\mathbf{i}– 8\mathbf{j}\ \</math> and <math>\ \ \mathbf{ r}_{0}=6\mathbf{i}+2\mathbf{j}</math>.
+
We have <math>\mathbf{a}=0\textrm{.}2\mathbf{i}+0\textrm{.}3\mathbf{j},\ \</math> <math>\mathbf{u}=4\mathbf{i}– 8\mathbf{j}\ \</math> and <math>\ \ \mathbf{ r}_{0}=6\mathbf{i}+2\mathbf{j}</math>.
The most suitable equation to use is <math>\mathbf{v}=\mathbf{u}+\mathbf{a}t\ \</math>.
The most suitable equation to use is <math>\mathbf{v}=\mathbf{u}+\mathbf{a}t\ \</math>.
-
Substituting the above values gives a vector eqaution for <math>t</math>.
+
Substituting the above values gives a vector equation for <math>t</math>.
-
<math>4\textrm{.}8\mathbf{i}-6\textrm{.}8\mathbf{j}=4\mathbf{i}– 8\mathbf{j}+(4\mathbf{i}– 8\mathbf{j})t\ \</math>
+
<math>4\textrm{.}8\mathbf{i}-6\textrm{.}8\mathbf{j}=4\mathbf{i}-8\mathbf{j}+(0\textrm{.}2\mathbf{i}+0\textrm{.}3\mathbf{j})t\ \</math>
 +
 
 +
0r <math>4\textrm{.}8\mathbf{i}-6\textrm{.}8\mathbf{j}=(4+0\textrm{.}2t\ )\mathbf{i}+ (0\textrm{.}3t-8\ )\mathbf{j}\ \</math>
 +
 
 +
Is there a <math>t</math> which satisfies both the <math>\mathbf{i}</math> terms and the <math>\mathbf{j}</math> terms?
 +
 
 +
<math>4\textrm{.}8\mathbf{i}=(4+0\textrm{.}2t\ )\mathbf{i}\ \</math>
 +
 
 +
and
 +
 
 +
<math>-6\textrm{.}8\mathbf{j}=(0\textrm{.}3t-8\ )\mathbf{j}\ \</math>
 +
 
 +
It is easily seen that <math>t=4 \ \text{s}</math> satisfies both these equations.

Current revision

We have \displaystyle \mathbf{a}=0\textrm{.}2\mathbf{i}+0\textrm{.}3\mathbf{j},\ \ \displaystyle \mathbf{u}=4\mathbf{i}– 8\mathbf{j}\ \ and \displaystyle \ \ \mathbf{ r}_{0}=6\mathbf{i}+2\mathbf{j}.

The most suitable equation to use is \displaystyle \mathbf{v}=\mathbf{u}+\mathbf{a}t\ \.

Substituting the above values gives a vector equation for \displaystyle t.

\displaystyle 4\textrm{.}8\mathbf{i}-6\textrm{.}8\mathbf{j}=4\mathbf{i}-8\mathbf{j}+(0\textrm{.}2\mathbf{i}+0\textrm{.}3\mathbf{j})t\ \

0r \displaystyle 4\textrm{.}8\mathbf{i}-6\textrm{.}8\mathbf{j}=(4+0\textrm{.}2t\ )\mathbf{i}+ (0\textrm{.}3t-8\ )\mathbf{j}\ \

Is there a \displaystyle t which satisfies both the \displaystyle \mathbf{i} terms and the \displaystyle \mathbf{j} terms?

\displaystyle 4\textrm{.}8\mathbf{i}=(4+0\textrm{.}2t\ )\mathbf{i}\ \

and

\displaystyle -6\textrm{.}8\mathbf{j}=(0\textrm{.}3t-8\ )\mathbf{j}\ \

It is easily seen that \displaystyle t=4 \ \text{s} satisfies both these equations.

Retrieved from "http://wiki.sommarmatte.se/wikis/2009/bridgecoursemechanics/index.php/Solution_8.4c"