Hong Kong

Stage 4 - Stage 5

The height $h$`h`, in metres, reached by a ball thrown in the air after $t$`t` seconds is given by the equation $h=10t-t^2$`h`=10`t`−`t`2.

a

Fill in the following table of values for $h=10t-t^2$`h`=10`t`−`t`2.

$t$t |
$1$1 | $2$2 | $3$3 | $4$4 | $5$5 | $6$6 | $7$7 | $8$8 | $9$9 | $10$10 |

$h$h |
$\editable{}$ | $16$16 | $\editable{}$ | $24$24 | $\editable{}$ | $\editable{}$ | $\editable{}$ | $16$16 | $\editable{}$ | $0$0 |

b

Graph the relationship $h=10t-t^2$`h`=10`t`−`t`2.

Loading Graph...

c

Determine the height of the ball after $5.5$5.5 seconds have elapsed.

d

What is the maximum height reached by the ball?

Easy

Approx 6 minutes

A satellite dish is parabolic in shape, with a diameter of $8$8 metres. Incoming signals are reflected to one collection point, the focus of the parabola, marked as point $F$`F` on the diagram (not to scale). The focus is positioned such that the focal length is $4$4 metres.

A parabolic antenna has a cross-section of width $16$16 m and depth of $2$2 m. All incoming signals reflect off the surface of the antenna and pass through the focus at $F$`F`. Note: Image is not to scale

When an object is thrown into the air, its height above the ground is given by the equation $h=193+24s-s^2$`h`=193+24`s`−`s`2, where $s$`s` is its horizontal distance from where it was thrown.

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