Chapter 8, Problem 17STP

(a)

To determine

To Find: The expression that shows the height of the rocket in factored form.

Answer to Problem 17STP

The factored for of function is $h(t)=-8t(2t-25)$

Explanation of Solution

Given information:

The equation provided is $h(t)=-16t^2+200t$

Rewrite the function as :

  $h(t)=-16t^2+200t$

  $h(t)=-8t(2t-25)$

(b)

To determine

To Find: The time at which height of the rocket is 0m

Answer to Problem 17STP

Height of the rocket is $0\text{m}$ when $t=12.5\text{sec}$

Explanation of Solution

Set $h(t)$ to 0 and solve for $t$ to get the times

  $h(t)=0$

  $-16t^2+200t=0$

  $-8t(2t-25)=0$

  $-8t=0$ and $(2t-25)=0$

  $t=0$ and $t=\frac{25}{2}$

Therefore, the height of the rocket is 0m when $t=\frac{25}{2}$

(c)

To determine

To Find: The greatest height reached by the model rocket and when does it occur.

Answer to Problem 17STP

The greatest height achieved by rocket is at time $t=6.25\text{sec}$

Explanation of Solution

The greatest height is achieved at the vertex $t=\frac{-b}{2a}$

For $h(t)=-16t^2+200t,$ , the values are

  $b=200$ and $a=-16$

  $t=\frac{-200}{2(-16)}$

  $t=\frac{200}{32}$

  $=6.25\text{sec}$

Hence the greatest height achieved by rocket is at time $t=6.25\text{sec}$