A stone was thrown from the top of a vertical cliff. The height, $h$ metres, of the stone above se

Question

A stone was thrown from the top of a vertical cliff. The height, $h$ metres, of the stone above sea level $t$ seconds after it is released can be modelled by the equation $h = 9t + 20 - 3t^2$.\nSome corresponding values of $t$ and $h$ are given in the table below.

$t$	$0$	$1$	$2$	$3$	$4$	$5$	$6$
$h$	$20$	$26$	$26$	$20$	$8$	$-10$	$-34$

State the height of the cliff.
[1]
On the grid, draw the graph of $h = 9t + 20 - 3t^2$ for $0 \le t \le 6$.
[2]
Use your graph in part (b) to estimate
1. the maximum height of the stone above sea level and the time at which this occurs,
  [2]
2. the length of time at which the stone is more than $23\text{ m}$ above sea level.
  [2]

Accepted Answer

(a) $20\text{ m}$ (b) Plot and join these points smoothly: $(0,20),(1,26),(2,26),(3,20),(4,8),(5,-10),(6,-34)$. The graph is a downward-opening parabola. (c)(i) $\text{Maximum height } \approx 26.8\text{ m}$,$\text{Time } \approx 1.5\text{ s}$ (c)(ii) $\text{Time } \approx 2.2\text{ s}$

Algebraic Expressions, Identities and Formulae

Algebraic Expressions, Identities and Formulae

Solution:

Solution locked