$\"\"$

\

The parametric equation of path of projectile motion is $\"\"$ and $\"\"$ .

\

Here $\"\"$ is the initial velocity.

\

$\"\"$ is the angle made with respect to ground.

\

$\"\"$ is the height above the ground.

\

(a)

\

The height above the ground is $\"\"$ feet.

\

Initial speed is $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in parametric equations.

\

$\"\"$ and $\"\"$ .

\

The parametric equations are $\"\"$ and $\"\"$ .

\

$\"\"$

\

(b)

\

The parametric equations are $\"\"$ and $\"\"$ .

\

The horizontal angle is $\"\"$ .

\

$\"\"$ and $\"\"$

\

$\"\"$ and $\"\"$

\

$\"\"$ and $\"\"$ .

\

Graph:

\

Graph the parametric equations $\"\"$ and $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

When $\"\"$ , $\"\"$ .

\

Hence its is not a home run.

\

$\"\"$

\

(c)

\

The parametric equations are $\"\"$ and $\"\"$ .

\

The horizontal angle is $\"\"$ .

\

$\"\"$ and $\"\"$

\

$\"\"$ and $\"\"$

\

$\"\"$ and $\"\"$ .

\

Graph:

\

Graph the parametric equations $\"\"$ and $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

When $\"\"$ , $\"\"$ .

\

Hence its is a home run.

\

$\"\"$

\

(d)

\

The parametric equations are $\"\"$ and $\"\"$ .

\

Find the minimum angle for a hit to be Home run.

\

For a hit to be home run, $\"\"$ and $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Let $\"\"$ .

\

$\"\"$ .

\

Graph:

\

Graph the function $\"\"$ :

\

$\"\"$

\

Observe the graph:

\

The solutions of $\"\"$ is $\"\"$ and $\"\"$ .

\

$\"\"$ is not considered since we require minimum angle.

\

$\"\"$ .

\

$\"\"$

\

Minimum angle is $\"\"$

\

$\"\"$

\

(a) The parametric equations are $\"\"$ and $\"\"$ .

\

(b) It is not a home run.

\

(c) It is a home run.

\

(d) Minimum angle is $\"\"$