7. Exercises
From Mechanics
| 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?
