Optimization Approach Using Calculus

We define our variables again.

Input := 


vnaught= 300;

x[t_, theta_]=vnaught * Cos[theta] *t; 

y[t_, theta_]=-16t^2 + vnaught* Sin[theta] *t;

We determine the range function by determining the x coordinate for the time t (Solve[ y[t,theta]==0,t]) at which the projectile strikes the ground.

We plot the range function to estimate the value of theta which gives a maximum range.

Thus it appears that at about Pi/4 or near .75 radians we have a maximum range. To determine the value of theta which maximizes this range precisely we determine where range'[theta]=0, i.e. where the derivative with respect to theta is 0.

We thus see that the maximum range of 2812.5 feet occurs when our angle of elevation theta is .785398 which is (as we see below) actually Pi/4.