ProjMotion.mws

Define Equation 3.12

>    eqn3_12 := x = v[i] * cos( theta[i] ) * t;

eqn3_12 := x = v[i]*cos(theta[i])*t

Define Equation 3.13

>    eqn3_13 := y = v[i] * sin( theta[i] ) * t - 1/2 * g * t^2;

eqn3_13 := y = v[i]*sin(theta[i])*t-1/2*g*t^2

Eliminate 2 from the equations, storing the result n a variable "tmp"

>    tmp := eliminate( {eqn3_12, eqn3_13}, t );

tmp := [{t = x/v[i]/cos(theta[i])}, {2*y*v[i]^2*cos(theta[i])^2-2*sin(theta[i])*x*v[i]^2*cos(theta[i])+g*x^2}]

The are 2 solutions. The first is trivial and we ignore it. We solve the second solution for y:

>    solve( tmp[2], y);

{y = -1/2*x*(-2*sin(theta[i])*v[i]^2*cos(theta[i])+g*x)/v[i]^2/cos(theta[i])^2}