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Derive an equation for displacement of a...

Derive an equation for displacement of a projectile fired at an angle `theta` from the ground.

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Displacement of a Projectile :
Suppose a body is projected up with an initial velocity u in a direction making an angle `theta` with the ground.
Resolving u in horizontal `(u_(x))` and vertical components `(u_(y))`:
`" "u_(x)=ucostheta, u_(y)usintheta`

For horizontal motion, `u_(x)=ucostheta`
By using equation
`" "x="horizontal velocity" times "time"`
`" "x =ucostheta times t`
`" "t=x/(ucostheta)`
For vertical motion
`" "u_(y)=usintheta,"acceleration" a_(y)=g`
Now, using equation
`" "s=ut+1/2at^(2)`
`" "y=usintheta(x/(ucostheta))+1/2(-g) times (x/(ucostheta))^(2)`
`" "y=xtantheta-1/2(gx^(2))/(u^(2) cos^(2)theta)`
`" "y=xtantheta-(gx^(2))/(2u^(2)cos^(2)theta)`
This equation represents a parabola.
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