The parametric equations are and

(a)

Consider .

Solve for .

.

substitute in .

.

is a quadratic function of , the graph of the parametric equation represents the parabola.

The general form of quadratic function is .

Compare the equation with general form.

and and .

(b)

Show that the projectile hits the ground when time .

When the projectile hits the ground the distance .

Equate to zero.

or .

The time period should not be zero.

Hence .

.

Therefore, the projectile hits the ground when time .

(c)

Find the  projectile distance when it strikes the ground.

The projectile hits the ground when time .

Substitute in .

Therefore, the projectile travelled horizontally when it hit the ground.

(d)

Find the time when .

Equate the parametric equations and .

or .

The time period is should not be zero.

Hence .

.

Find the horizontal and vertical distances at .

Substitute in .

.

Since .

.

Find the values of .

Substitute and .

.

The projectile travels up a plane inclined at to the horizontal.

If the value of then the value of , thus the absolute value is not needed.

(a) The graph of the parametric equations represents the parabola.

(b) The projectile hits the ground when time .

(c) The projectile travelled horizontally when it hit the ground.

(d) and if the value of then the value of , thus the absolute value is not needed.