Chapter 7.4, Problem 73PPS

a.

To determine

To find the velocity of a roller coaster at the top of 225-foot hill to achieve velocity of 120 feet per second at the bottom.

Answer to Problem 73PPS

  $v_{{}_0}=0$

Explanation of Solution

Given:

Velocity of the coaster at the top of the hill is represented by the formula,

  $v_{{}_0}=\sqrt{v^2-64h}$ where $v_{{}_0}$ is the velocity of the coaster at the top of the hill and h the height of the hill and v velocity in feet per second at the bottom of the hill.

Calculation:

Let $v=120$ and $h=225$

Substitute in the given function to find the velocity if the coaster at the to of the hill.

  $\begin{array}{l}\Rightarrow v_{{}_0}=\sqrt{{120}^2-64(225)}\\ \Rightarrow v_{{}_0}=\sqrt{14400-14400}\\ \Rightarrow v_{{}_0}=\sqrt{0}\\ \Rightarrow v_{{}_0}=0\end{array}$

Conclusion:

Therefore, roller coaster will have a velocity zero at the top of the hill.

b.

To determine

To explain the reason for the given statement is false.

Answer to Problem 73PPS

False

Explanation of Solution

Given:

  $v_{{}_0}=\sqrt{v^2-64h}$

The given statement is false, since the square root is for the whole term and not for individual terms.

This would be possible only if there is a square root for individual terms.

Conclusion:

Therefore, the given statement is false.