$\"\"$

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

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

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

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

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(a)

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

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Consider $\"\"$ .

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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The rectangular equation is $\"\"$

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$\"\"$

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(b)

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The rectangular equation is $\"\"$ .

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Compare the equation with $\"\"$

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Here $\"\"$ .

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$\"\"$

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Find $\"\"$ .

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$\"\"$

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$\"\"$

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Initial velocity is $\"\"$ .

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

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

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

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

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

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$\"\"$

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(c)

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

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The rectangular equation is $\"\"$ .

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Graph:

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

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Graph the rectangular equation $\"\"$ .

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$\"\"$

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Observe the graph:

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

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$\"\"$

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(d)

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The rectangular equation is $\"\"$ .

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Find the maximum height.

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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/

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

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

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Find the range.

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Range is the horizontal distance travelled during projectile motion.

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Graph:

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Graph the rectangular equation $\"\"$ .

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$\"\"$

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Observe the graph:

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Maximum height is $\"\"$ .

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Range is $\"\"$ .

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$\"\"$

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

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

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

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

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(d)

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Maximum height is $\"\"$ .Range is $\"\"$ .