Question

a ball is dropped from an 80 - m building. the height (in meters) after t sec is given by h(t)=-4.9t^{2}+80. (a) find h(1) and h(1.5). (b) interpret the meaning of the function values found in part (a). part: 0 / 4 part 1 of 4 (a) h(1)=□

Explanation:

Step1: Substitute t = 1 into h(t)

Substitute \(t = 1\) into \(h(t)=-4.9t^{2}+80\). So \(h(1)=-4.9\times(1)^{2}+80\).

Step2: Calculate h(1)

\[

$$\begin{align*} h(1)&=-4.9\times1 + 80\\ &=-4.9+80\\ &=75.1 \end{align*}$$

\]

Step3: Substitute t = 1.5 into h(t)

Substitute \(t = 1.5\) into \(h(t)=-4.9t^{2}+80\). So \(h(1.5)=-4.9\times(1.5)^{2}+80\).

Step4: Calculate h(1.5)

\[

$$\begin{align*} h(1.5)&=-4.9\times2.25 + 80\\ &=-11.025+80\\ &=68.975 \end{align*}$$

\]

Step5: Interpret the function - values

\(h(1) = 75.1\) means that 1 second after the ball is dropped, the height of the ball is 75.1 meters above the ground. \(h(1.5)=68.975\) means that 1.5 seconds after the ball is dropped, the height of the ball is 68.975 meters above the ground.

Answer:

(a) \(h(1)=75.1\), \(h(1.5)=68.975\)
(b) \(h(1) = 75.1\) means the ball's height 1 - second after being dropped is 75.1 m above the ground. \(h(1.5)=68.975\) means the ball's height 1.5 - seconds after being dropped is 68.975 m above the ground.