Chapter 9.5, Problem 23E

To determine

To find the time to reach 5feet height.

Answer to Problem 23E

Time to reach 5feet height is 1.79sec.

Explanation of Solution

Given:

Equation:

  $h=-16t^2+26t$

Time to reach 5feet height.

Calculation:

According to question

  $h=-16t^2+26t$

Also,

  $h=5$

Therefore,

  $5=-16t^2+26t$

Converting the equation in standard form:

  $16t^2-26t-5=0$

On comparing the equation with $a{t}^2+bt+c$

  $a=16,b=-26,c=-5$

Finding the value of $t$

  $t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substituting the values,

  $t=\frac{-(-26)\pm \sqrt{{(-26)}^2-4(16)(-5)}}{2(16)}$

Opening brackets,

  $t=\frac{26\pm \sqrt{676-320}}{32}$

So,

  $t=\frac{26\pm \sqrt{996}}{32}$

Solving root

  $t=\frac{26\pm 31.55}{32}$

So,

  $t=\frac{26+31.55}{32}$ and $t=\frac{26-31.55}{32}$

So,

  $t=\frac{57.55}{32}$ and $t=\frac{5.55}{32}$

Therefore,

  $t=1.79$ and

  $t=-0.17$

Time can never be negative so, time to reach 5feet height is 1.79sec.