Chapter 7.4, Problem 51PPS

a.

To determine

To simplify the formula.

Answer to Problem 51PPS

  $v=8\sqrt{h}$

Explanation of Solution

Given:

  $v=\sqrt{64h}$

h is the height of the hill in feet.

v is the velocity of roller coaster in feet per second at the feet of the hill.

Calculation:

Now,

  $\begin{array}{l}\Rightarrow v=\sqrt{64h}\\ \Rightarrow v=\sqrt{8\times 8\times h}\\ \Rightarrow v=\sqrt{8\times 8}\times \sqrt{h}\\ $ \Rightarrow v={(8^2)}^{\frac{1}{2}}\times \sqrt{h}$\Rightarrow v=8\sqrt{h}\end{array}$

Conclusion:

Hence, the simplified form is $v=8\sqrt{h}.$

b.

To determine

To determine the velocity of roller coaster at the bottom of a 134 foot hill.

Answer to Problem 51PPS

92.6 feet per second

Explanation of Solution

Given:

  $v=8\sqrt{h}$

h is the height of the hill in feet.

v is the velocity of roller coaster in feet per second at the feet of the hill.

Calculation:

Let,

  $v=8\sqrt{h}\mathrm{..............................}(i)$

Given, heightof the hill is 134 foot, which means, $h=134$ .

Now substituting the value of h in equation ( i ),

  $\Rightarrow v=8\sqrt{134}$

  $\begin{array}{l}\Rightarrow v=8\times 11.5758\\ \Rightarrow v=92.6\end{array}$

Conclusion:

Hence, the required velocity is 92.6 feet per second.