Chapter 3.4, Problem 16E

To determine

To find: The time to get bullet back down in each case.

Answer to Problem 16E

Time to get bullet back down in moon is $320\sec$ and for earth is $52\sec$.

Explanation of Solution

Given information: In this question, equation of height for moon is $s=832t-2.6t^2$ and equation of height for earth is $s=832t-16t^2$ , using this we want to find the time to get bullet back down in each cases.

Calculation: For finding time to reach bullet at maximum height, we will equate instantaneous velocity equal to zero. And for finding bullet to get back down on each case we will multiply two times in time where bullet reaches at maximum height.

1. For Moon,

  $\begin{array}{l}\frac{ds}{dt}=832-5.2t\\ \frac{ds}{dt}=0\\ t=160\sec \\ T=2*160=320\sec \end{array}$

2. For Earth,

  $\begin{array}{l}\frac{ds}{dt}=832-32t\\ \frac{ds}{dt}=0\\ t=26\sec \\ T=2*26=52\sec \end{array}$

Thus, the correct answer is, Time to get bullet back down in moon is $320\sec$ and for earth is $52\sec$.