Question

A frog sitting on a stump 3 feet high hops off and lands on the ground.

During its leap, its height h in feet is given by h= -0.5d^2 + 2d + 3, where d

is the distance from the base of the stump. How far is the frog from the

base of the stump when it landed on the ground? *

Answer 1

Answer: The distance of frog from the  base of the stump is 5.16 feet ( approx)

Step-by-step explanation:

Given, A frog sitting on a stump 3 feet high hops off and lands on the ground.

During its leap, its height h in feet is given by $h= -0.5d^2 + 2d + 3$, where $d$  is the distance from the base of the stump.

When the stump landed on the ground, h= 0 .

So put h=0 in the given equation , we get

$0=-0.5d^2 + 2d + 3\\\\\Rightarrow\ 0.5d^2-2d-3=0$

Multiply both sides by 2 , we get

$d^2-4d-6=0\\\\\Rightarrow\ d=\dfrac{-(-4)\pm\sqrt{4^2-4(1)(-6)}}{2(1)}\\\\=\dfrac{4\pm\sqrt{16+24}}{2}\\\\=\dfrac{4\pm\sqrt{40}}{2}\\\\=\dfrac{4\pm2\sqrt{10}}{2}=2\pm\sqrt{10}$

$i.e.\ d=2-\sqrt{10}\ \ or\ \ d=2+\sqrt{10}\\\\\ i.e. d=2-3.1622\ \ or\ \ d=2+3.1622\\\\ i.e. d= -1.1622\ \ or\ \ d=5.1622\approx5.16$

Since , distance cannot be negative.

Hence, the distance of frog from the  base of the stump is 5.16 feet ( approx).