Chapter 6, Problem 3QC

To determine

To Find :

The time taken by the ball to reach the ground, assuming there is no air resistance.

Answer to Problem 3QC

1 to 2 seconds

Explanation of Solution

Given Information:

Allie drops a ball from the top of a 30-foot building.The formula is $h(t)=-16t^2+h_0$ where t is the time in seconds and the initial height $h_0$ is in feet.

Concept Used :

The roots of an equation are the x -coordinates of the points at which the related graph of the equation intersects the x -axis .

Calculation:

  $\begin{array}{l}\text{Given}\\ h(t)=-16t^2+h_0\\ h_0=30\text{ feet}\\ h(t)=0=\text{height of the ball when it is on the ground}\text{.}\\ \text{So, the equation is }-16t^2+30=0\\ \text{We observe the roots of the equation from the related graph}\text{.}\end{array}$

Graph:

  

So, from the graph , we can find the root.

Since, the time is always non-negative.

Hence the time taken by the ball to reach the ground is between 1 to 2 seconds.