Answer
$a.$
$H(1)=15.1$ meters
$H(1.1)=14.071$ meters
$H(1.2)=12.944$ meters
$H(1.3)=11.719$ meters
$b.$
$H(x)=15 \Rightarrow x\approx 1.01$ seconds
$H(x)=10\Rightarrow x\approx 1.43$ seconds
$H(x)=5\Rightarrow x\approx 1.75$ seconds
$c.$
$H(x)=0\Rightarrow x\approx 2.02$ seconds
Work Step by Step
$\mathrm{a}$.
$\left[\begin{array}{ll}
x & H(x)\\
1 & H(1)=20-4.9(1)^{2}\\
& =20-4.9\\
& =15.1\\\\
1.1 & H(1.1)=20-4.9(1.1)^{2}\\
& =20-4.9(1.21)\\
& =14.071\\\\
1.2 & H(1.2)=20-4.9(1.2)^{2}\\
& =20-4.9(1.44)\\
& =12.944\\\\
1.3 & H(1.3)=20-4.9(1.3)^{2}\\
& =20-4.9(1.69)\\
& 11.719
\end{array}\right]$
$b.$
Solve for x when
$\left[\begin{array}{lll}
H(x)=15 & \Rightarrow & 15=20-4.9x^{2}\\
& & -5=-4.9x^{2}\\
& & x=\sqrt{5/4.9}\\
& & x\approx 1.01\\\\
H(x)=10 & \Rightarrow & 10=20-4.9x^{2}\\
& & -10=-4.9x^{2}\\
& & x=\sqrt{10/4.9}\\
& & x\approx 1.43\\\\
H(x)=5 & \Rightarrow & 5=20-4.9x^{2}\\
& & -15=-4.9x^{2}\\
& & x=\sqrt{15/4.9}\\
& & x\approx 1.75
\end{array}\right]$
$c.$
The rock strikes the ground $\Rightarrow$ its height is 0.
$\left[\begin{array}{lll}
H(x)=0 & \Rightarrow & 0=20-4.9x^{2}\\
& & -20=-4.9x^{2}\\
& & x=\sqrt{20/4.9}\\
& & x\approx 2.02\\
& &
\end{array}\right]$
