Define Equation 3.12. I would call the name "eqn3_12" or maybe "eqn3.13" but Mathematica doesn't like the underscore or period in variable names.

In[1]:=

eqn12 = x == v _ i Cos[ θ _ i ] t

Out[1]=

x == t Cos[θ _ i] v _ i

Define Equation 3.13

In[2]:=

eqn13 = y == v _ i Sin[ θ _ i ] t - 1/2 g t^2

Out[2]=

y == -(g t^2)/2 + t Sin[θ _ i] v _ i

Solve the equations for y, eliminating t:

In[3]:=

Solve[ {eqn12, eqn13}, y, t ]

Out[3]=

{{y -> (x Sec[θ _ i]^2 (-g x + Sin[2 θ _ i] v _ i^2))/(2 v _ i^2)}}

Converted by Mathematica  (September 16, 2003)