Question

if a rock falls from a height of 39 meters on earth, the height h (in meters) after x seconds is approximately h(x)=39 - 4.9x^{2}. (a) what is the height of the rock when x = 1.8 seconds? the height of the rock when x = 1.8 seconds is meters. (round to three decimal places as needed.) (b) when is the height of the rock 10 meters? the height of the rock is 10 meters when x≈ seconds. (round to two decimal places as needed.) (c) when does the rock strike the ground? the rock strikes the ground when x≈ seconds. (round to two decimal places as needed.)

Explanation:

Step1: Substitute x = 1.8 into H(x)

$H(1.8)=39 - 4.9\times(1.8)^{2}$
$=39-4.9\times3.24$
$=39 - 15.876$
$=23.124$

Step2: Set H(x) = 10 and solve for x

$10 = 39-4.9x^{2}$
$4.9x^{2}=39 - 10$
$4.9x^{2}=29$
$x^{2}=\frac{29}{4.9}$
$x=\sqrt{\frac{29}{4.9}}\approx2.43$ (we take the positive value since time can't be negative)

Step3: Set H(x) = 0 and solve for x

$0 = 39-4.9x^{2}$
$4.9x^{2}=39$
$x^{2}=\frac{39}{4.9}$
$x=\sqrt{\frac{39}{4.9}}\approx2.82$ (we take the positive value since time can't be negative)

Answer:

(a) 23.124
(b) 2.43
(c) 2.82