Chapter 4.5, Problem 53PPS

a.

To determine

Find the time taken by firework from lit to explode.

Answer to Problem 53PPS

  $8\frac{1}{3}\sec onds$

Explanation of Solution

Given information:

A firework’s distance $d$ meters from the ground is $d=-1.5t^2+25t$ where $t$ is the number of seconds after lit the firework.

Calculation:

Consider equation. $d=-1.5t^2+25t$

Apply equation,

  $\begin{array}{l}x=-\frac{b}{2a}\left[\therefore a=-1.5b=25\right]\\ so,\\ t=-\frac{b}{2a}\\ =-\frac{25}{2\left(-1.5\right)}\\ =\frac{25}{3}\\ t=8\frac{1}{3}\sec onds\end{array}$

Hence, firework explode after, $8\frac{1}{3}\sec onds$

b.

To determine

Find the height firework to explode.

Answer to Problem 53PPS

  $104meters$

Explanation of Solution

Given information:

A firework’s distance $d$ meters from the ground are $d=-1.5t^2+25t$ where $t$ the number of seconds after lit the firework is.

Calculation:

Consider equation. $d=-1.5t^2+25t$

Put $t=8\frac{1}{3}$ in $d=-1.5t^2+25t$

  $\begin{array}{l}d=-1.5{\left(\frac{25}{3}\right)}^2+25\left(\frac{25}{3}\right)\\ d=-104.16+208.33\\ d=104.2\end{array}$

Hence, height of firework when explode is, $104meters$