Question

To avoid hitting any rocks below, a cliff diver jumps up and out. The equation h = -16t2 + 4t + 26 describes her height h in feet t seconds after jumping. Find the time at which he returns to a height of 26 feet.

Answer 1

The time at which cliff diver returns to a height of 26 feet is 0.25 second

Solution:

Given, To avoid hitting any rocks below, a cliff diver jumps up and out.

The equation
`\mathrm{h}=-16 \mathrm{t}^(2)+4 \mathrm{t}+26` describes her height h in feet t seconds after jumping.

We have to find the time at which he returns to a height of 26 feet.

Now, h = 26,

Then, substitute h value in given equation

`\begin{array}{l}{26=-16 t^(2)+4 t+26} \\\\ {\rightarrow 16 t^(2)-4 t=26-26} \\\\ {\rightarrow 4 t(4 t-1)=0}\end{array}`

4t ≠ 0 as t can’t be 0

`\begin{array}{l}{\rightarrow 4 t-1=0} \\\\ {\rightarrow 4 t=1} \\\\ {\rightarrow t=(1)/(4)}\end{array}`

Hence, at 0.25 second he is at 26 feet height.