Chapter 4.5, Problem 40E

To determine

How long it will take the rock to reach the bottom of the Grand Canyon.

(Hint: The distance to the bottom of the canyon is − 1750 meters from the rim.)

Answer to Problem 40E

19.3 sec

Explanation of Solution

Given information: Physics: The distance $d\left(t\right)$ fallen by a free-falling body can be modeled by the formula $d\left(t\right)=v_{0}t-\frac{1}{2}g{t}^2,$ where $v_0$ is the initial velocity and g represents the acceleration due to gravity. The acceleration due to gravity is 9.8 meters per second squared. If a rock is thrown upward with an initial velocity of + 4 meters per second from the edge of the North Rim of the Grand Canyon, which is 1750 meters deep.

Calculation:

Fill in the constants for gravity and depth

  $4t-\frac{1}{2}\left(9.8\right)t^2=-1750$

Bring terms to 1 side

  $-4.9t^2+4t+1750=0$

Multiply out the negative

  $4.9t^2-4t-1750=0$

Use quadratic formula

  $t=\frac{-\left(-4\right)\pm \sqrt{{\left(-4\right)}^2-4\left(4.9\right)\left(-1750\right)}}{2\left(4.9\right)}$

Simplify

  $t=\frac{4\pm \sqrt{34,316}}{9.8}$

  $t=-18.5,19.3$

19.3 seconds.