Chapter ISG, Problem 9.6STP

To determine

To find maximum height, time to reach water and plot graph .

Answer to Problem 9.6STP

  $t=0.25$ second attain maximum height

Maximum height

  $h(0.25)=9$

Time to reach water

  $t=1$

  

Explanation of Solution

Given information:

  $h{(t)}_{}=-16t^2+8t+8$

Calculation:

A parabola reaches its maximum value at its vertex, or turning point. Use the formula for the axis of symmetry to find the x -coordinate of the vertex.

  $t=\frac{-8}{2(-16)}$

On solving,

  $t=0.25$

On solving,

  $t=0.25$ second attain maximum height

Maximum height

  $h(0.25)=-16{(0.25)}^2+8(0.25)+8$

On solving,

  $h(0.25)=-2^4\times 2^{-4}+2+8$

On solving,

  $h(0.25)=-1+2+8$

On solving,

  $h(0.25)=9$

Time to reach water

  $h{(t)}_{}=0$

  $0=-16t^2+8t+8$

On solving,

  $2t^2-t-1=0$

On solving,

  $2t^2+t-2t-1=0$

On solving,

  $t(2t+1)-1(2t+1)=0$

On solving,

  $(2t+1)(t-1)=0$

On solving,

  $(2t+1)=0$

  $(t-1)=0$

On solving,

  $t=-\frac{1}{2}$

  $t=1$

Time cannot be negative

Hence, $t=1$

Graph

  $h{(t)}_{}=-16t^2+8t+8$

Let $h{(t)}_{}=y$

Let $t=x$

Table is given below