Hello, Eponine!

You are expected to know the "free fall formula":

. .

where: . = height of the object, = initial height of the object,

= initial velocity of the object.

We have: .You are standing on a bridge over a creek, holding a stone 20 ft. above the water

(a) You release the stone. .How long will it take the stone to hit the water?

The equation is: .

"Hit the water" means the height of the stone is zero.

When is ?

. .

Therefore, the stone hits the water at: seconds.

We have: .You take another stone and toss it straight up with an initial velocity of 30 ft/sec.

How long will it take the stone to hit the water?

The equation is: .

When is ?

. .

Quadratic Formula: .

Therefore, the stone hits the water at: . seconds.

The equation is: .If you throw a stone straight up in the air with the initial velocity of 50 ft/sec,

could the stone reach a height of 60 ft. above the water?

There are at least two ways to answer this question. .(The answer is NO.)

[1] When is ?

. . .

Quadratic Formula: . no real roots

Therefore, the stoneneverreaches a height of 60 feet.

[2] The graph of is a down-opening parabola.

. . .Its maximum point occurs at its vertex.

The vertex occurs at: .

We have: .

The vertex is: .

When feet.

The maximum height is only feet.

. . Itneverreaches 60 feet.