Accedmychevron_right11thchevron_rightmathchevron_rightFunctions And Graphschevron_rightExercise 2.1

Solution

Given:

h(x)=4010x2h(x)=40-10x^2

(i) Heights at given times

h(1)=4010(1)2=30h(1.5)=4010(1.5)2=4010(2.25)=17.5h(1.7)=4010(1.7)2=4010(2.89)=11.1\begin{aligned} h(1)&=40-10(1)^2=30\\ h(1.5)&=40-10(1.5)^2=40-10(2.25)=17.5\\ h(1.7)&=40-10(1.7)^2=40-10(2.89)=11.1 \end{aligned} h(1)=30 m,h(1.5)=17.5 m,h(1.7)=11.1 m\boxed{h(1)=30\text{ m},\quad h(1.5)=17.5\text{ m},\quad h(1.7)=11.1\text{ m}}

(ii) When does the stone strike the ground?

Set h(x)=0h(x)=0:

4010x2=010x2=40x2=4x=240-10x^2=0\Rightarrow 10x^2=40\Rightarrow x^2=4\Rightarrow x=2

(Time is non-negative.)

x=2 seconds\boxed{x=2\text{ seconds}}