The parametric equations for a projectile with constant gravity g: 

\[x = v_0 t \cos \theta + x_0\]

\[y = -\frac{1}{2} gt^2 + v_0 t \sin \theta + y_0\]

ex. A shell is fired from ground level with an initial speed of 768 ft/sec. at an angle of 30°. Find: 

1. \(\vec{r}(t)\) 

2. the maximum altitude attained 

3. the range of the shell 

4. the speed on impact 

5. the horizontal distance when \(y = 2240\) ft.