Question

a ball is dropped from an 80 - m building. the height (in meters) after t sec is given by h(t)=-4.9t² + 80. (a) find h(1) and h(1.5). (b) interpret the meaning of the function values found in part (a).

Explanation:

Step1: Substitute $t = 1$ into $h(t)$

$h(1)=-4.9\times(1)^2 + 80$
$h(1)=-4.9+80$
$h(1)=75.1$

Step2: Substitute $t = 1.5$ into $h(t)$

$h(1.5)=-4.9\times(1.5)^2 + 80$
$h(1.5)=-4.9\times2.25 + 80$
$h(1.5)=-11.025+80$
$h(1.5)=68.975$

Step3: Interpret $h(1)$

The ball's height 1 second after being dropped is 75.1 meters.

Step4: Interpret $h(1.5)$

The ball's height 1.5 seconds after being dropped is 68.975 meters.

Answer:

(a) $h(1) = 75.1$, $h(1.5)=68.975$
(b) $h(1)$ represents the height of the ball 1 second after it is dropped from the 80 - m building, which is 75.1 meters. $h(1.5)$ represents the height of the ball 1.5 seconds after it is dropped from the 80 - m building, which is 68.975 meters.