Chapter 3.1, Problem 67E

To determine

To determine about which rock will hit the ground first.

Answer to Problem 67E

On Jupiter the rock will hit the ground first.

Explanation of Solution

Given information:

  

Given equation is,

  $h=-\frac{g}{2}{t}^2+h_0$

Now the value of $g$ are given for different planets.

Let,

  $\begin{array}{l}{g}_e=32\\ g_m=12\\ g_j=76\end{array}$

From the given equation put $h=0$ we get,

  $\begin{array}{l}0=-\frac{g}{2}{t}^2+h_0\\ h_0=\frac{g}{2}{t}^2\\ t=\pm \sqrt{\frac{2h_0}{g}}\end{array}$

Now we know time is positive we get,

  $t=\sqrt{\frac{2h_0}{g}}$

Now we can observe that greater the value of g, less the value of time as both are inversely proportional.

Hence the smallest value of time shall be given by the greatest value of g.(which is of Jupiter)

Hence on Jupiter the rock will hit the ground first.