I am trying to find the maximum range of projectile from an elevation. I found the answer in this question, but I have two questions:
- Why does $y$ need to be $0?$
- Why do they differentiate with respect to $\theta,$ and what is the meaning of this?
classical-mechanicsintuitionkinematicsphysicsprojectile motion
I am trying to find the maximum range of projectile from an elevation. I found the answer in this question, but I have two questions:
Best Answer
Because the projectile's range $R$ is its horizontal distance travelled, which is precisely its $x$-coordinate at its landing point, that is, when there is no elevation, that is, when $y=0.$
The projectile's range $R$ varies according to its launch angle $\theta,$ so is maximised when $\frac{\mathrm dR}{\mathrm d\theta}$ equals zero. (Consider the graph of $R$ against $\theta;$ $R$ attains its maximum value when its gradient $\frac{\mathrm dR}{\mathrm d\theta}$ equals zero.)
P.S. I am the author of the cited Question; even though I accepted Patrick's Answer, please treat my self-Answer there as the natural continuation of the work that I'd started in the Question.