7. Exercises
From Mechanics
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</div>{{#NAVCONTENT:Answer a|Answer 7.1a|Answer b|Answer 7.1b|Answer c|Answer 7.1c|Solution a|Solution 7.1a|Solution c|Solution 7.1c}} | </div>{{#NAVCONTENT:Answer a|Answer 7.1a|Answer b|Answer 7.1b|Answer c|Answer 7.1c|Solution a|Solution 7.1a|Solution c|Solution 7.1c}} | ||
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| + | ===Exercise 7.2=== | ||
| + | <div class="ovning"> | ||
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| + | Two children, A and B, run so that their position vectors in metres at time | ||
| + | <math>t</math> | ||
| + | seconds are given by: | ||
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| + | <math>{{\mathbf{r}}_{A}}=t\mathbf{i}+\frac{9t}{2}\mathbf{j}</math> | ||
| + | and | ||
| + | <math>{{\mathbf{r}}_{B}}=t\mathbf{i}+(9t-{{t}^{2}})\mathbf{j}</math> | ||
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| + | Plot the paths of the two children for | ||
| + | <math>0\le t\le </math>4.5 | ||
| + | . What happens when | ||
| + | ''t''=4.5? | ||
| + | |||
| + | |||
| + | </div>{{#NAVCONTENT:Answer|Answer 7.2|Solution|Solution 7.2}} | ||
Revision as of 15:07, 11 September 2009
| Theory | Exercises |
Exercise 7.1
A football ball is kicked so that its position, in metres, at time t seconds is given by
\displaystyle \mathbf{r}=6t\mathbf{i}+\left( 15t-4.9{{t}^{2}} \right)\mathbf{j}
where \displaystyle \mathbf{i} and \displaystyle \mathbf{j} are horizontal and vertical unit vectors respectively.
a) Find the position of the ball when t = 0, 1, 2, 3 and 4 seconds.
b) Plot the path of the ball.
c) From your plot estimate the horizontal distance travelled by the ball when it hits the ground.
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Exercise 7.2
Two children, A and B, run so that their position vectors in metres at time
\displaystyle t
seconds are given by:
\displaystyle {{\mathbf{r}}_{A}}=t\mathbf{i}+\frac{9t}{2}\mathbf{j}
and
\displaystyle {{\mathbf{r}}_{B}}=t\mathbf{i}+(9t-{{t}^{2}})\mathbf{j}
Plot the paths of the two children for
\displaystyle 0\le t\le 4.5
. What happens when
t=4.5?
