MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

The time at which cliff diver returns to a height of 26 feet is 0.25 secondSolution:Given, To avoid hitting any rocks below, a cliff diver jumps up and out. The equation [tex]\mathrm{h}=-16 \mathrm{t}^{2}+4 \mathrm{t}+26[/tex] 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
[tex]\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}[/tex]4t ≠ 0 as t can’t be 0[tex]\begin{array}{l}{\rightarrow 4 t-1=0} \\\\ {\rightarrow 4 t=1} \\\\ {\rightarrow t=\frac{1}{4}}\end{array}[/tex]Hence, at 0.25 second he is at 26 feet height.