Chapter 6, Problem 2E

To determine

To Find:

The time when the object will reach a height of 10,000 feet.

Answer to Problem 2E

B

Explanation of Solution

Given Information:

An object is shot straight upward into the air with an initial speed of 800 feet per second. The height h that the object will be after t seconds is given by the equation $h=-16t^2+800t$ .

Calculation:

  $\begin{array}{l}Given\\ h=-16t^2+800t\\ and\\ h=10,000\\ \text{Substitute the value of h in the equation and solve for t:}\\ 10000=-16t^2+800t\\ \text{⇒}16t^2-800t+10000=0\\ \text{⇒}16t^2-400t-400t+10000=0\\ \text{⇒}4t(4t-100)-100(4t-100)=0\\ \text{⇒}(4t-100)(4t-100)=0\\ $ \Rightarrow {(4t-100)}^2=0$\text{⇒}4t-100=\mathrm{0..........}[{\text{ a}}^2=0\iff a=0]\\ \text{⇒}t=\frac{100}{4}\mathrm{..............}[\text{add 100 each side then divide each side by 4]}\\ \text{⇒}t=25\\ \text{So, the object will reach a height of 10,000 feet after 25 seconds}\text{.}\\ \text{Hence, B is the correct option}\text{.}\end{array}$