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Solution 8.1a

From Mechanics

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Current revision (12:16, 27 March 2011) (edit) (undo)
 
(4 intermediate revisions not shown.)
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In this case we have
In this case we have
<math>\mathbf{u}=4\mathbf{i}</math>
<math>\mathbf{u}=4\mathbf{i}</math>
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,
+
and
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<math>\mathbf{a}=0.9\mathbf{i}+0.7\mathbf{j}</math>
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<math>\mathbf{a}=0\textrm{.}9\mathbf{i}+0\textrm{.}7\mathbf{j}</math>
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and
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<math>{{\mathbf{r}}_{0}}=400\mathbf{i}+350\mathbf{j}</math>.
+
-
Substituting these into the equation
+
Substituting these into the equation
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<math>\mathbf{r}=\mathbf{u}t+\frac{1}{2}\mathbf{a}{{t}^{\ 2}}+400\mathbf{i}+350\mathbf{j}</math>
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<math>\mathbf{v}=\mathbf{u}+\mathbf{a}t \ \</math>
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gives the position vector of the ball at time <math>10</math> as:
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gives the velocity of the jet-ski at time <math>t=10 \text{ s }</math> as:
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+
 
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<math>\begin{align}
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<math>\mathbf{v}=4\mathbf{i}+(0\textrm{.}9\mathbf{i}+0\textrm{.}7\mathbf{j})\times 10</math>
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& \mathbf{r}=(4\mathbf{i})\times 10+\frac{1}{2}(0.9\mathbf{i}+0.7\mathbf{j})\times {{10}^{\ 2}}+400\mathbf{i}+350\mathbf{j} \\
+
 
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& =40\mathbf{i}+45\mathbf{i}+35\mathbf{j}+400\mathbf{i}+350\mathbf{j} \\ \\
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which gives
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& =485\mathbf{i}+385\mathbf{j} \ \text{m}
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\end{align}</math>
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<math>\mathbf{v}=13\mathbf{i}+7\mathbf{j} \ \text{ m}{{\text{s}}^{\text{-1}}}</math>

Current revision

In this case we have u=4i and a=0.9i+0.7j

Substituting these into the equation v=u+at   gives the velocity of the jet-ski at time t=10 s as:

v=4i+(0.9i+0.7j)10

which gives

v=13i+7j  ms-1