$\"\"$

\

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)

\

Eliminate parameter $\"\"$ from the parametric equations.

\

Consider $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The rectangular equation is $\"\"$

\

$\"\"$

\

(b)

\

The rectangular equation is $\"\"$ .

\

Compare the equation with $\"\"$

\

Here $\"\"$ .

\

$\"\"$

\

Find $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Initial velocity is $\"\"$ .

\

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

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ .

\

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

\

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

\

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

\

$\"\"$

\

(c)

\

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

\

The rectangular equation is $\"\"$ .

\

Graph:

\

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

\

Graph the rectangular equation $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

The graphs obtained parametric equations is equal to the rectangular equations.

\

$\"\"$

\

(d)

\

The rectangular equation is $\"\"$ .

\

Find the maximum height.

\

The maximum height of a object in a projectile trajectory occurs when the vertical component of velocity, v_y, equals zero. Source: Boundless. “Key Points: Range, Symmetry, Maximum Height.” Boundless Physics. Boundless, 08 Jan. 2016. Retrieved 09 Mar. 2016 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/two-dimensional-kinematics-3/projectile-motion-42/key-points-range-symmetry-maximum-height-230-11284/

\

Maximum height of a object in a projectile motion occurs when vertical component of velocity is zero.

\

In simple, this is a point where we draw the line of symmetry.

\

Find the range.

\

Range is the horizontal distance travelled during projectile motion.

\

Graph:

\

Graph the rectangular equation $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

Maximum height is $\"\"$ .

\

Range is $\"\"$ .

\

$\"\"$

\

(a) The rectangular equation is $\"\"$

\

(b) $\"\"$ , $\"\"$ and $\"\"$ .

\

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

\

(c) The graphs obtained parametric equations is equal to the rectangular equations.

\

(d)

\

Maximum height is $\"\"$ .

\

Range is $\"\"$ .