Answer
(a) The height for the rock after 1 second is 7 meters. The height for the rock after 1.1 seconds is 4.27 meters. The height for the rock after 1.2 seconds is 1.28 meters.
(b) The height of the rock is 15 meters after about 0.62 seconds. The height of the rock is 10 meters after about 0.88 seconds. The height of the rock is 5 meters after about 1.07 seconds.
(c) The rock strikes the ground after about 1.24 seconds.
Work Step by Step
(a) Replace x by the time:
$H(1)=20-13(1)^2=20-13=7$
$H(1.1)=20-13(1.1)^2=20-15.73=4.27$
$H(1.2)=20-13(1.2)^2=20-18.72=1.28$
(b) Replace H(x) by the heights:
$15=20-13x^2\rightarrow-5=-13x^2\rightarrow x^2=\frac{5}{13}\rightarrow x\approx0.62$
$10=20-13x^2\rightarrow-10=-13x^2\rightarrow x^2=\frac{10}{13}\rightarrow x\approx0.88$
$5=20-13x^2\rightarrow-15=-13x^2\rightarrow x^2=\frac{15}{13}\rightarrow x\approx1.07$
(c) Find x when H(x) is zero:
$15=20-13x^2\rightarrow-20=-13x^2\rightarrow x^2=\frac{20}{13}\rightarrow x\approx1.24$
