$\"\"$

\

The speed of a ball is $\"\"$ .

\

The height is $\"\"$ .

\

The angle is $\"\"$ .

\

The value of $\"\"$ .

\

(a)

\

Time as a parameter in parametric equations are $\"\"$ and $\"\"$ .

\

Substitue the values in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

The parametic equation is $\"\"$ instead of $\"\"$ to see the vertical motion better.

\

Substitute the values in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Therefore, the parametric equations of the ball as a function of time are $\"\"$ and $\"\"$ .

\

$\"\"$

\

(b)

\

Find the length of the ball in the air.

\

The ball is in the air untill $\"\"$ .

\

Equate $\"\"$ to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ or $\"\"$ .

\

$\"\"$ or $\"\"$ .

\

The time is always postive.

\

Therefore, the ball is in the air for $\"\"$ seconds.

\

$\"\"$

\

(c)

\

Find the time when the ball is in the maximum height.

\

The maximum height occurs at the vertex of the quadratic function.

\

The maximum height is at $\"\"$ .

\

The quadratic equation is $\"\"$ .

\

The general form of quadratic equation is $\"\"$ .

\

Compare the equation with general form.

\

Here $\"\"$ , $\"\"$ and $\"\"$ .

\

Substitute $\"\"$ , $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

The maximum height occurs at $\"\"$ seconds.

\

substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Therefore, the maximum height is $\"\"$ .

\

$\"\"$

\

(d)

\

Graph:

\

Graph the function $\"\"$ .

\

$\"\"$

\

$\"\"$

\

(a) The parametric equations of the ball as a function of time are $\"\"$ and $\"\"$ .

\

(b) The ball is in the air for $\"\"$ seconds.

\

(c) The maximum height is $\"\"$ is occurs at $\"\"$ .

\

(d)

\

$\"\"$