Chapter 8.3, Problem 22Q

a.

To determine

To find: after how many seconds does the pinecone hits the ground.

Answer to Problem 22Q

After 1.25 seconds

Explanation of Solution

Given information:

The heighty (in feet) of a pineconet seconds after falling from a tree is given by the function:

  $y=-16t^2+25$   ..... (1)

Calculation:

When the pinecone hits the ground its height is 0 feet.

Substituting $y=0$ in equation (1),

  $\begin{array}{c}y=-16t^2+25\\ 0=-16t^2+25\\ 16t^2=25\end{array}$

  $\begin{array}{c}{t}^2=\frac{25}{16}\\ t=\pm \sqrt{\frac{25}{16}}\\ t=\pm \frac{5}{4}\\ t=\pm 1.25\end{array}$

Now, here t represents time and time can never be negative, so solution is $t=1.25$ .

Conclusion:

The pinecone hits the groundafter 1.25 seconds.

b.

To determine

To find:which pinecone hits the ground in least amount of time.

Answer to Problem 22Q

First pineconehits the ground in least amount of time.

Explanation of Solution

Given information:

The heighty (in feet) of a pineconet seconds after falling from a tree is given by the function:

  $y=-16t^2+25$   ..... (1)

Second pineconefalls from a height of 36 feet.

The constant term 25 in the equation (1) gives the initial height of the first pinecone.

Thus, the first pinecone falls from a height of 25 feet and the second pinecone falls from a height of 36 feet.

It is obvious that the pinecone which falls from a lower height will hit the ground earlier.

Thus, thefirst pineconehits the ground in least amount of time.