From Mechanics

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Revision as of 17:24, 12 April 2010

In this case we have \displaystyle \mathbf{u}=4\mathbf{i} , \displaystyle \mathbf{a}=0\textrm{.}9\mathbf{i}+0\textrm{.}7\mathbf{j} and \displaystyle {{\mathbf{r}}_{0}}=400\mathbf{i}+350\mathbf{j}.

Substituting these into the equation \displaystyle \mathbf{r}=\mathbf{u}t+\frac{1}{2}\mathbf{a}{{t}^{\ 2}}+400\mathbf{i}+350\mathbf{j} gives the position vector of the ball at time \displaystyle t=10 \text{ s } as:

\displaystyle \begin{align} & \mathbf{r}=(4\mathbf{i})\times 10+\frac{1}{2}(0\textrm{.}9\mathbf{i}+0\textrm{.}7\mathbf{j})\times {{10}^{\ 2}}+400\mathbf{i}+350\mathbf{j} \\ & =40\mathbf{i}+45\mathbf{i}+35\mathbf{j}+400\mathbf{i}+350\mathbf{j} \\ \\ & =485\mathbf{i}+385\mathbf{j} \ \text{m} \end{align}