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)

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=(-(-4)\pm√(4^2-4(1)(-6)))/(2(1))\\\\=(4\pm√(16+24))/(2)\\\\=(4\pm√(40))/(2)\\\\=(4\pm2√(10))/(2)=2\pm√(10)`

`i.e.\ d=2-√(10)\ \ or\ \ d=2+√(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).