Chapter 9.8, Problem 24PPS

(a)

To determine

To calculate: To graph the function for a waterfalls.

Explanation of Solution

Given information: The function $d=-16t^2+h$ models the distance $d$ in feet a drop of water falls $t$ seconds after it begin its descent from the top of a waterfall of height $h$

Tallest U.S Waterfalls
Waterfall	State	Height (m)
Olo’upena Falls	Hawaii	900
Pu’uka’oku Falls	Hawaii	840
Waihilau	Hawaii	792
Colonial Creek Falls	Washington	788
Johannesburg Falls	Washington	751

Calculation:

Given the function $d=-16t^2+h$ models the distance $d$ in feet a drop of water falls $t$ seconds after it begin its descent from the top of a waterfall of height $h$

Consider the waterfall Johannesburg Falls

Height of waterfall $h=751$

Thus, the function becomes:

  $d=-16t^2+751$

When $t=1$

  $\begin{array}{l}d=-16{\left(1\right)}^2+751\\ d=-16+751\\ d=735\end{array}$

When $t=2$

  $\begin{array}{l}d=-16{\left(2\right)}^2+751\\ d=-16\left(4\right)+751\\ d=-64+751\\ d=687\end{array}$

When $t=3$

  $\begin{array}{l}d=-16{\left(3\right)}^2+751\\ d=-16\left(9\right)+751\\ d=-144+751\\ d=607\end{array}$

When $t=4$

  $\begin{array}{l}d=-16{\left(4\right)}^2+751\\ d=-16\left(14\right)+751\\ d=-256+751\\ d=495\end{array}$

Plotting the graph of the function:

  

Conclusion:

Hence, graph for waterfall is plotted

(b)

To determine

To calculate: To find the time taken by drop of water to reach the river at the base of waterfall

Answer to Problem 24PPS

Time taken by drop of water to reach the river at the base of Johannesburg waterfall is approximately $7$ seconds

Explanation of Solution

Given information: The function $d=-16t^2+h$ models the distance $d$ in feet a drop of water falls $t$ seconds after it begin its descent from the top of a waterfall of height $h$

Tallest U.S Waterfalls
Waterfall	State	Height (m)
Olo’upena Falls	Hawaii	900
Pu’uka’oku Falls	Hawaii	840
Waihilau	Hawaii	792
Colonial Creek Falls	Washington	788
Johannesburg Falls	Washington	751

Calculation:

Given the function $d=-16t^2+h$ models the distance $d$ in feet a drop of water falls $t$ seconds after it begin its descent from the top of a waterfall of height $h$

Consider the waterfall Johannesburg Falls

Height of waterfall $h=751$

Thus, the function becomes:

  $d=-16t^2+751$

Time taken by drop of water to reach the river at the base of Johannesburg waterfall is calculated by substituting $d=0$ in above equation:

  $\begin{array}{l}0=-16t^2+751\\ 16t^2=751\\ t^2=\frac{751}{16}\\ t^2=46.94\\ t=6.85\\ t\approx 7\end{array}$

Conclusion:

Hence, time taken is approximately $7$ seconds